I know the real answer to this question is to get a pro fit, but until I have time to do that...

I find myself having to readjust backwards on the saddle every few minutes in order to get comfortable.
E.g., it feels like I've slid forward. Is my saddle too far forward, too far back, tipped down too much, or too high? I've tried adjusting it in a couple directions but fear I'm just making things worse.

I move around on the saddle depending on effort and circumstance. Sometimes you have to accept that you are going to be on the rivet

That is a fit problem, but some saddles need a little nose up tilt to put you in the sweet spot. You should not be sliding forward.

I would say start with a little nose up, then try moving the saddle forward.

Yep ... try tipping the nose of the saddle up a bit.

Skateboard tape?

Actually, it depends on what is making you "uncomfortable".

^^ +1

Years ago I found that the only way to cure this problem was swapping in a shorter stem. The bike was an older Marinoni but the reach was just a bit long, and my body wanted to be forward when it was time to hammer.

Was having the same problem. Resolved it by revisiting the bike fitter at my LBS.

First off, yes, get a bike fit.

Until then, FIRST make your saddle level, like acutally use a level to make sure it's straight. Play around with different positions.
Obviously a sprint in the drops will make your hips roll forward and will have a different position when riding straight up in the tops.

[TABLE]
[TR]
[TD="class: word"]on the rivet [/TD]
[TD="class: tools"][/TD]
[/TR]
[TR]
[TD][/TD]
[TD="class: text, colspan: 3"]Extreme physical exertion to the point of almost giving up. Derived from bike racing in the olden days when bike seats had rivets, and in an effort not to get dropped one would slide forward on the saddle to exert maximum pressure on the pedals so as to hang on the the amphetamine-loaded Belgian in front of you.
Person 1: So how'd you do?
Person 2: Dude, I was on the rivet for like an hour until I finally blew.
[/TD]
[/TR]
[/TABLE]

personally, if the saddle is already 'level', as in good support at the sitzbones, I'm never crazy about tilting it up further into the luggage.
If I'm having to move forward, and it's not because I'm dialin it up to 400 watts, then usually dropping the saddle about 3-5mm works for me... in a pinch. Then when I get a chance, I rethink my height and fore/aft position on that bike.
pushing any gear usually causes you to get driven back, but getting over the top of a big gear at higher rpms (100 and +), while in the saddle, will pull you forward, like a TT position.
Might want to define when it's happening to you.
How did you 'decide' on your current position?
The cockpit setup is usually secondary, while your saddle to cranks setup will be primary to a balanced position.

It's been said but tip the nose up. I tide all over my saddle but never "slide" around. Hills or harder effort with lower cadence I move back. If I'm spinning extra fast and/ or descending I move forward .

saddle too wide or too narrow can cause this.

I have a couple pair of bib shorts (purchased from the same place - one of those Websites out of China) that are just plain more slippery than any other bibs I've ever had, and have me sliding forward all the time. My saddle (WTB Pure V Race) is level. No other bibs I have do this. For me, it's a little bothersome but not enough to ruin my rides and not enough not to wear them? I just slide back when I need to.

If you're constantly pushing back on the saddle, even if you're not riding hard, the saddle may be too far back. Your bars may be too close too. You may want to experiment with your saddle position.

It would be best to have someone look at your position, even if it's just an informal glance by a more experienced and established rider. Often they can spot major position flaws right away.