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I have a situation like that on one of my routes.
Here I am riding north (up) on the main road. It used to be that the freeway off-ramp that comes in on the bottom right merged with the through lanes. I would shoot a gap and get into the shoulder. Then they realigned the road such that the off-ramp becomes a third RTOL lane (zero shoulder) up to the next intersection. Since then I will split the lanes. Exact positioning depends, but tend to ride mainly on the RTOL side of the dashed lane divide. I think in that area the road is signed for 35, but most of it is 45 and traffic tends to average 45-50, unless it's congested.
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I will confess that I haven't read the whole thread before posting just the OP and a few following posts and then very lightly skimmed down through the rest. I'll come back later and do so (pressed for time at the moment). I don't normally do this (posting without reading completely first) but I did want to tell the OP how I handle this exact kind of situation myself.
What I personally do in this exact kind of situation the OP describes depends on the speed of the road and the width of the lanes:
Low speed road (25-mph or less speed limit) then I use the right most straight through lane and hold the lane like I own it. Even if some idiots start doing crazy things around me accordingly so long as I'm not in immediate mortal danger I pay them no mind and do what I know is right and the best option which for me on a low speed road means almost always taking the exact same lane position as I would on a motorcycle with the only exception being something that really slows me down like going up a big hill or something. Otherwise I won't even shoulder edge ride period on such a low speed road. You think I'm going too slow cycling at 20-mph or just slightly more on a 25-mph speed limit road, tough, deal with it. If I get slowed down I'll try to move over if I can safely do so but otherwise I'm going fast enough compared to the speed of the road. Heck I've been know to switch to the fast lane and pass cars in down-town traffic on a bicycle because those long streams of big metal boxes where blocking up the slow lane and going annoyingly slower then I could go and I could keep up with the fast lane traffic in-town.
High speed road with narrow lanes, but a good shoulder where a RTOL cuts into the shoulder edge I'm riding on and I'm going straight through not turning right then I start edging in real close to the white line when approaching where the right turn lane starts while giving my "don't right hook me hand signal" until the RTOL is fully developed and there is a solid separation line between it and the adjacent right most straight through lane and then put both hands back on the bars and ride straight through the RTOL and across the intersection to the shoulder edge and continue on my merry way shoulder edge riding as before. I hold position in the RTOL far enough left in that lane that its fairly obvious I'm going straight through but not so far to the left that car drivers are tempted to try to squeeze around me on my right side. About left wheel track or so.
High speed road with wide lanes, and a good shoulder where a RTOL cuts into the shoulder edge I'm riding on and I'm going straight through not turning right then I start edging in real close to the white line when approaching where the right turn lane starts while giving my "don't right hook me hand signal" and hold that position until the RTOL is fully developed and there is a solid separation line between it and the adjacent right most straight through lane and then put both hands back on the bars and ride straight down that white line between the RTOL and the adjacent right most straight through lane and across the intersection to the shoulder edge and continue on my merry way shoulder edge riding as before. I only do that riding the line between the two lanes if the lanes are wide enough that I could have motor vehicles in both lanes on both sides of me safely passing me at the same time and still have enough room myself. Whether the lanes are wide enough to do that does vary depending on the vehicles so when approaching a right hand turn lane I do check behind me and size up the vehicles that could pass me while I'm negotiating where the RTOL is looking for any wider then normal ones like big trucks and buses or wide trailers.
As to my "don't right hook me hand signal" I use that's not an official hand signal in the left hand only signal system but one I've made up over the years that seems to get the message across fairly well. Left hand out and the whole arm down in a 45-degree angle with palm flat open. Like the left hand turn signal only with the arm not pointing straight out but rather down and out at a 45-degree angle. Works good if you use the left hand only signal system and in my experience is worthy addition. Obviously some drivers don't care no matter what you do as far as signals but for those who do notice them and respond it seems to do the trick nicely.
As to the legality of a straight through cyclists riding in the left side of a RTOL and going straight through in that position. A few state law codes actually do specify that specifically as a valid and legal option for cyclists and moped riders and such who are edge riding. Most do not, mine is one of the states that does not and its technically illegal but I do it anyway as being the "right" thing to do even if it isn't legal and so far its one of the few things that I have never had the cops harass me for as to how I ride my bike on the roads up here and I've even done it a couple of times that way with a cop car right behind me or passing me and they don't seem to mind at all and especially like me to do it that way when they are one of the ones that can pass me easier as a result of me doing it that way. Same is generally true of most motorists in general as well although I did get yelled at once by a motorists who didn't like me going straight from the left edge of the RTOL (something along the lines of "right turn only you *%$@!" is what he yelled) but that only happened once so far in many years of riding that way where as I get yelled at to get off the road and such all the time.
Riding the white line between the lanes (lane splitting) is not technically illegal in my state but also is not specifically designated as legal either. So I'm on a little better legal footing when the lanes are wide enough to allow me to ride the white line then when they are narrow and I go straight through in the left wheel track of the RTOL. And after all if they are wide enough to allow me to ride the white line and let not only the faster straight through traffic pass me easily but also allow faster traffic in the right turn lane to also pass me on my other side as well I am okay with that (oh, yes, on a long right hand turn lane especially motorists up here do go 45+ mph down a right hand turn lane if they can) and I see no reason to be a jerk and slow up the right turn lane if there is enough width to allow me to ride the line and let both side pass me. If there isn't enough width for that though then I will slow up the right turn lane and ride in the left tire track on it.
Better option then the straight through lane on a high speed roadway where I'm shoulder edge riding until a right turn lane cuts into the shoulder edge, at least in my experience.