other than contract costs, is it better to rapidly promote players to get better coaching as long as they get playing time , or will poor performance slow
progression

No one can give a definitive answer.    Personally, I do it like this:

S1(the partial season):    RL/LoA/HiA
S2  HiA/AA
S3 AA/AAA
S4 AAA/BL

The exceptions are players I'll have in the bigs by S3 or if I have a craptastic coach at a specific level.   I might demote before ST to get a player with a more favorable coach. 

I'm not disputing that progression.  It's one I have used more or less.  I posted a thread earlier, however, in which I asked whether there was any penalty or slower development that occurs when promoting a player to the ML's as soon as their ratings were competitive.  Answers on that thread indicated confidently that there wasn't and that players develop just as well in the majors.  I'll bump it for comparison.

Not disputing that.    Which is why I said "Personally" and "no definitive answer".

Yep.  My memory of that thread was different than what was included.  Though others certainly sounded more confident.  Have you ever taken your best or one of your best prospects and stuck him in the majors right away or way earlier than usual as a test? (full disclosure:  I'm not a highly successful owner and don't expect I would have the guts to take that risk given that I've had so few really good prospects in my experience).

FWIW, for a long while I've been putting my top draft picks/young IFA into AA or AAA (depending on which has better coaches and an open position) and their development has been solid. I pretty much punt coaching at Rookie/Low-A and sometimes Hi-A.

Some who started at 18 and are now in the majors (OVR Ratings season-by-season until development stalls):

Joshua Stone 61-67-73-75-76-77 for P with 36 PAT/67 MU
Kosuke Aoki 51-58-64-69-70-71-72 for P with 64/79
Ozzie Graham 66-76-83-86-87-87-88 for SS/3B 75/98
Wayne Walden 59-68-74-78-79-80 SS 63/58

Stone took an unfortunate hit when I didn't realize that "demote before ST" means "demote before a ST game is scheduled."
I don't see any sign that being overmatched does harm. But that's an opinion and hard to test. With the new draft fuzziness, it's more likely to obtain two similar players of the same age. If that happens, I'll put one in Low-A and one in AAA and see what difference there is after a few seasons. Coaching should give the AAA guy some benefit, but if age/level matters that should offset it.

For the owners that do promote mid season, which I see is a lot. How long do you generally wait before putting that top prospect up a level? After the all star break? Set number of games?

I won't start my best prospects any higher than AA. But if they show good performance at that level, and they would start at the next level up and get better coaching, I sometimes promote them 'mid-season' (no specific time. Just whenever I remember to look to see how they're doing).