prgsocdem
Also, don't worry about companies or recruiters bad-mouthing you to one another. It rarely happens for legal reasons.
About phones:
For phone issues, consider using google voice on your laptop with a headset ($10) and fixed Google voice number instead- this will be hard when you're on the move (can forward calls), but it will make sure you can occasionally have high-quality phone calls. I almost never needed to accept or make non-scheduled phone calls during my job search. To sign up unfortunately you'll need at least temporary access to get a verification call on a mobile or landline (but hopefully the shelter or a public phone can help with this).
Depending on how big a volume of possessions you need to carry with you, scout out all the Starbucks (which now allow use of their wifi and bathrooms without purchase) in a reasonable distance, to find one or two with quiet corners where you could take an interview. If the interviewers hear sound in the background, tell them you're in a Starbucks. If they ask why, say your roommates are loud so you tend to work from Starbucks. There shouldn't be any further questions about that.
Unfortunately, though, @jl2718 is right that many employers won't look upon OP's situation positively, and it's hard to tell if any will (except @leesalminen, who apparently will). Therefore some strategic non-disclosure of circumstances is advised.