I agree with VoxVim! Playing stronger players is an excellent way to improve your game. I have made the mistake of constantly playing with weaker players in the past, but with ChessMood I had the opportunity to play much stronger players and drastically improve my rating. I suggest you check ChessMood out!
Advice for an old beginner
@1
"I've been playing 60-minute time limit." ++ Better play with increment, like 45|15.
"Would it make sense to play without any rating limits" ++ Yes.
"I don't mind getting pummeled by a stronger player if it helps me improve." ++ Good.
"it should gravitate to a reasonably accurate level no matter who I play against." ++ Correct.

I agree with most that have been said, but be careful to not become a "cannonfodder". We have all seen the boxing star punch down sparring rookies, boosting his confidence.

I agree with most that have been said, but be careful to not become a "cannonfodder". We have all seen the boxing star punch down sparring rookies, boosting his confidence.
Are you sure you wanted to post this here? This is chess.com, not boxing.com.

Yes. it's a metaphor used at higher IQ-levels, meaning: Don't be a punchbag for higher rated chessplayers.

It just doesnt translate though. Chess isnt boxing and playing against a stronger player doesnt cause brain damage or anything like that.

Losing to stronger players can be a valuable learning experience. Analyzing your games, understanding where you went wrong and learning from your mistakes can help you identify areas for improvement and refine your skills.
I am an older player myself, Here are two pieces of advice that I can give you that I wish someone had given me
As adults, we have learned to read and absorb information and master abstract concepts. It's easy to think that gaining more and more knowledge will help us improve rapidly. WRONG! in chess, skill is much more important than knowledge. It is more important to learn how to calculate, to visualize variations before they are played, to keep your pieces protected, than to understand a lot of theoretical stuff.
Don't be too proud to read and study chess material aimed at kids! We may have a lifetime of knowledge and accomplishments to be proud of, but when it comes to chess, we are beginners, and the best chess material for beginners is written with kids in mind. Jeff Coakley's "Winning Chess Exercises for Kids," and Murray Chandler's "How to Beat Your Dad at Chess" are goldmines of just the kind of skill building material you need
Being older, my mind isn't as quick as it once was. But if I take my time and focus, I do okay. So I've been playing 60-minute time limit. I've been playing live chess by setting a rating range of 50 points below and above my own. Would it make sense to play without any rating limits (either above or below) for my opponents? I don't mind getting pummeled by a stronger player if it helps me improve. And as far as my rating goes, I think it should gravitate to a reasonably accurate level no matter who I play against.