I think that's the crucial point. Maybe buy in with $60 and then endeavour to double up, cash out and then later (having played some blackjack or had a meal in between, so it's not too obvious) buy in at another table with $60, so your initial investment is safely tucked in your pocket.
However once you have doubled up on the second table, why do you need to cash out and go to a third table? Your initial "investment" is already safely in your pocket, so you should continue playing there until you feel that it is no longer profitable, then go home.
Jumping from table to table is bad enough, but to reduce back down to $60 multiple times will inevitably be seen in a bad light. However I see no reason why you shouldn't start with $60 initially and if they don't like it, that's tough.
Here's the deal. You are only going to learn short stack poker, you're not going to get a lot of hands in, and once your stack gets to 200 BBs, you're going to have no idea what's going on and a guy like me is going to come in and eat you up. In the fifteen days I was home playing live games I took four or five pots down over 400 BBs because of opponents like you. And when I was learning the game, I made the same mistake.
You are only seeing one facet of poker, short stack poker. If you buy in to a 1/2 with $60, it's basically all-in on the flop at the latest on the first hand you decide to play. If you buy in for the full $200, you have a lot more room, and your big hands are going to get paid off. I won't play in games that have capped buy-ins below 100 BBs if I can help it, 100 BBs is close enough with a few plays and good hands I can be sitting at 200 BBs, and then I enter the profitable realm of deep-stack hunting. Guys who sit with 30 BBs when I have 250 BBs stacked up I'll call with garbage just to get a seat open.
Now, as for your behavior - it is common courtesy (and in a lot of card rooms, a house rule -) that if you cash out from a limit, and return to the limit in a certain number of time, you are expected to buy-in for the exact amount you left the table with. In online, it's harder to enforce, because one player can (and is authorized to) play ten tables at once, enforcing this is limited to just the table you leave.
The only times you should leave your table are when you find it is no longer profitable, you're not playing well, it's time to go, or the table breaks. If the table is not profitable and you want to play at a different table, you should let the floorperson know you want a table change. That crap you're doing would piss me off. However, I'd be very glad once your seat opened because somebody with more than 30 BBs could fill it.
If money is an issue for you, I would suggest you save up more of a bankroll, you're missing out on the most profitable part of poker by just playing short stack. While you'll still do a fist pump every time you flop middle set against TpTk with 30 BBs, just imagine how glorious that same pot would be with 100 BBs, or 200?
I play 2/3 NL in LA when I'm home, and the level play is far from unbeatable. I almost always know where I stand in the hand (poker intuition), and with my proper bankroll I rarely go on tilt.
If you want to take poker seriously as a way to make money, than I strongly suggest you add facets to your game other than the short stack hit and run. Not only will it make you unpopular, but it's simply not profitable, and makes you an easy target for bad beats. If I raise to 3 BBs, you reraise to 9 BBs, and I flop any draw, you can't bet enough to make me fold, because I get two cards to call your jam, and for all I know I could be ahead. And if I'm sitting with 200+ BBs, then rest assured, I'll be calling your measly bet with just about any draw or pair.
I strongly suggest you google deep stack poker, poker room courtesy (hell, ask a floor person), and implied
odds, as all of these are apparently missing from your game currently. Hell, look into bankroll management, as well.
For a seasoned player, the 1/2 NL games are probably weak enough that a regular with half a brain could tear them apart with only 5-10 Buy-ins, but it sounds like you're far from that.