I'm only "decent" at eyeballing distances because of all the fishing I did on different sized boats. Sounds stupid, but I'm pretty accurate at judging if something is 15-40 feet of distance from where I'm standing lol.
Anyway, BO, I'm sure that after I say this, you'll have some anecdotes of growing up poor and playing muni courses, but I'd wager that you've played on "good" golf courses almost your entire life. There are some serious dog tracks out there that a lot of the people that post here play every day where you would probably just raise your nose and say "nope" if someone offered to let you play for free
ON TOPIC: "flop" type shots don't necessarily have to be big long swings. You can make a smaller backswing with an open faced club and as long as you're accelerating through the shot and not 'giving up on it' through impact, you should be able to make a glancing blow to the ball. There may be some technical things you do in your short game stuff that may not allow you to do this properly, but in theory it's all just physics of collision at impact.