A.U,

If you file for H1 with your OPT  I-20, your H1 will be approved but they won't approve change of status and won't issue your H1 I-94. So even if you change to B2 or another F1 once you file, you need to go out of US to get your H1 stamp and I-94 or file for amendment later.

I don't recommend filing two petitions at the same time. Even if you want to file for B2, you need to wait until your H1 is decided so that you don't jeopardize your H1.

Also, I don't feel comfortable with B2. Going to B2 from F1 and again to F1 if H1 is not approved will definitely be complicated. I suggest that you maintain your F1 all the time. Here are your options:

1) If you can (ie. if you have enough savings to sustain until October) and are willing to forget about your OPT and more than 4 months pay, get a new I-20 now and file H1 with your new I-20. Joining English as a Second Language (ESL) classes is the only option you have as you have only 2 weeks now. If you do that or even join some other college, you actually need to attend classes to maintain status. So we are talking about more than 6 months here.

2) This I think will be best for you:

Apply for H1 with your current I-20 with Premium processing and start looking for schools to transfer for fall. Even if USCIS takes 1-2 months in the worst case  to issue you your receipt number, you should get your decision within May-June. So you'll still have some time in July plus your 60 day grace period (if you qualify) to decide your next move. Join ESL class (which I feel is the cheapest and easiest) or any other school and file for H1 amendment petition(to change status from your new F1 to H1 and issued your I-94) with your new I-20 as soon as your H1 is approved.

With your new I-20, you'll be in status until you amendment petition is approved. Supposing your H1 is approved within June and you file your amendment within July, you should get a decision before or during October. This is better as you can work until the end of your OPT and also might have to spend only 2-3 months for your ESL compared to 6 months in option 1.

After you get your new I-20, If you don't want to file the amendment petition, you can instead go to Canada or Mexico to get your stamp and I-94 so that you can start working on Oct 1, but going out is always risky.

You can email me if you think this is not clear as I feel there is too much information to be able to properly expain everything here.

P.S: Do not take anything explained here as legal advice and discuss all the options with your lawyer.