Don't get stuck thinking of just either/or this one thing.

What's the status of where you live now? (living situation A)? Tomorrow's choice we'll call situation B and HUD chit we'll call C.

What does A cost (just do your own worksheet) per month. What does B cost a month and what would C cost a month?

What is the ongoing cost of taking B? By that I mean, if you got B and it cost $500 a month and you had to take it for at least 12 months, that would be $6,000 a year. Now, if C came along after 4 months, so you had to take it within 6 months (60 days; are you sure that applies to your state? There might be slight differences in how soon you have to take advantage of it depending on the housing conditions in your area?) and C saved you $100/month, you'd "make" $600 the first year (the second set of 6 months) and if you only had to pay one months' rent to break your lease for B, that would still be a profit of $100 for the year (because you are paying $500 for A). However, if you had to pay 2 months rent to break your lease, you'd lose $400 ($1000 minus $600 less rent for C) but then next year you would gain that back as well as $800.

What, besides money, does C offer/cost? If you do not like the C choices (like I think I heard you say?), then they aren't really a choice? Can you work with B to accept a C voucher? Can you work with B to not charge you if you get a C voucher, put you on a month-to-month lease and promise you'll give them six weeks' notice instead of only four (since you'll have 8 weeks to use C so you decide within 2 but don't use it until all 8 weeks are done)?

What happens over time if you do "nothing" now, skip B and go from A to C? You use your time now to get better organized to move and your ducks in a row, sell some things, start a little savings account, etc.

Can you move into your boyfriend's apartment, move him out and take over the lease of his apartment? If you two have the goal of only living with him a month or so you could maybe put up with that/make things work well enough?

Can you move the stuff you want to sell into your boyfriend's apartment and worry about that after your move? Make room for it by throwing out some of his "junk" like is going to have to be done anyway. If you are doing it to make room for you/your stuff, it might not be as hard, there'll be more motivation?

Have you looked at choices D, some sort of shared living situation? If you are going to pay $600/month then that's around $20 a day; are there any trailer parks, okay motels, rooming houses, year-round campgrounds, etc. that charge that or a little more/less? Any way to do house-sitting for people going overseas (doctors, missionaries, etc.) or on extended vacation that might get you to C (and a little money)? Maybe you could find a bed-and-breakfast in two locations where half the year they don't have customers and would love someone for 6 months and the other would have the opposite problem (of course, you'd probably have to live with blizzards and blazing heat. . . since vacationers would want the opposite :-)