I have had a devil of a time with wear on the drive train...

Normally in one year on one bike I use 2 freewheels, 4 chainrings and 4 chains.

A new 3rd chain will skip over the cogs on hills or hard acceleration.

I have used Dura-Ace and Sachs chains.

I clean the chain weekly in a park chain cleaner and have tried various lubes including Tri-flow...

The picture that follows is of a freewheel after 6 months and 2 chains. (6000 to 7000 miles) Is this normal? Am I expecting too much? Back a few years my old 5 speed stuff never did this.

The newer cassettes do have thinner sprockets, and tend to not be as hard, so I'm not surprised you're seeing more chain wear.

IME one of the biggest factors affecting chain/sprocket life is chain tension. Higher tensions, mean more wear plain and simple. You get higher tensions from climbing with small sprockets, being heavier, riding faster (on average).

You can't do anything about your weight, and don't want to slow down, but you can think about gear selection. If you have a choice between long climbs with the inner ring and smaller rear sprockets, or outer/bigger the latter will improve chain life somewhat. Also, to the extent it's possible, try to spread sprocket use out over a few rather than one or two.

Given that you're riding a decent amount and going through drivetrains, consider rotating 3 chains on the same cassette, switching them out at regular intervals of less than 1,000 miles. This keeps the chain and sprocket wear condition better matched, and will push the point at which you start skipping. The multiple chain approach will yield more miles for your hardward buck.

Lastly, because I have to say this, (though you should consider the source) think about your chain lube. Higher tensions increase bearing and contact point pressure, and so call for a lubricant with higher film strength. Light riders in the plains can lube their chains with chicken soup and do OK, but powerful hill climbers need decent lubrication.

My events of choice are hill climb time trials, I just moved here from California.

I was at 4 days a week in the hills(1 of them with Como Street) and I am a hefty 217 with 10% body fat.

The other 3 are just flat land high speed runs of 40 miles or better.

I skip a day here and there depending on how I feel. I may miss one day a week.

So you closely meet my profile of someone who can expect lousy chain/sprocket life.

Don't change how you ride, and you can't change who you are, so focus of what you can change. I don't know the rest of your drivetrain, or gear selection, but consider combined larger chainrings and cassettes, If you can climb on that narrow cassette, consider a larger inner, with a slightly wider cassette, to move the climbing gear choices away from the level gear ones.

Also think about lubrication and rotating chains.

Let's be clear here, you are using the Sachs FW in the photo ?

If yes, I cannot tell much detail from the photo as it is too blurry. I can tell it's a Sachs by recognizing the profile, in the photo it's not legible.

I use Sachs FW's and have had for many many years, up and over many a heights. The cogs wear , well, not forever but they do not seem to wear much at all. If you are referring to the notches on the corners of the cogs, those are from ther factory to assist shifts. The only real wear I can make out, is on the large cog, and that seems to be the zinc plating, and not the shape of teeth.

Was this a brand new FW ?

I didn't clean my chains often when I used petroleum lubes, and never with the wax based one's I use now. Once a week cleaning ? Unless you are riding in filth, that is way to much.

If you look close there are spots on the sides of the cogs where the chain has widened the contact point on every tooth.

I have no idea what would cause this, as I have been using Sachs and Sun Tour Freewheels since the 80's and not seen what you are describing.

Was this a brand new Sachs FW ?

I think you are killing your chains with "kindness". Are you using a water based solvent in your Park cleaner? If so I expect you have gotten water into the inside of the chain and your Tri-Flow or what ever you lube with isn't displacing it. If you use an organic solvent like kerosene or OMS in the Park you have totally stripped any interior lube and I expect the outside lube hasn't replace if.

Frankly there is no reason to heavily clean a chain with anything like that frequency, particularly deep cleaning it a lot. You are doing more harm than good.

I can see those mashed spots on the teeth -- they remind me of the teeth of a softer aluminum chainring after it's been used a little. Either they didn't do a good job of hardening the sprockets, or you must be a beast on those hills.