How to schedule a second biometrics appointment for a UK visit visa?

1. Proceed to submit my passport and visa application to the UK consulate and hope they process it quickly and send me back my passport before my upcoming trip in 8 days time.

It might happen (although you might not want to rely on it): UK visit visa processing times for those applying from within the US:

General Visit (6 months or less): Most applications are processed within 15 days.

Number of days to process application* ::: % of applications decided
3 days ::: 2%
5 days ::: 9%
10 days ::: 75%
15 days ::: 97%
30 days ::: 99%
60 days ::: 100%

2. Wait until I return from my trip and at that point submit the application with a 25 day old biometric confirmation attached, and hope the consulate will accept it.

As @MrAndySweet commented, that may present problems:

Apply for a UK visa in the USA:

Your biometric confirmation receipt will be stamped at your appointment. You then have 5 days to post this, your application form, your passport and supporting documents to UK Visas and Immigration (UKVI).

3. Wait until I return from my trip and then start a whole new application, pay the fee again, get my biometrics taken again, and then submit.

That would be up to you, your finances, and plans for visiting the UK.

Any other options? Is there any way to schedule a second biometrics appointment after already having gone to the first one, so I don't have to start a whole new application?

Priority visa service

This is an optional service where you can pay an extra fee to fast track your application and have your visa application processed ahead of non priority applications.

You must pay for the priority visa service online on the VFS Global website before you post your application. The VFS User pay services page contains further information on how to apply, the fee and how to pay for this service.

The selections:

• Gold, $1600, next-business day processing (please take note of cut of times), no prior appointment required.
• Silver, $750, priority processing, usually within 5 working days, prior appointment required but not needed with payment of additional $75 walk in fee (accepted on first-come first-serve basis).
• Bronze, $310, standard processing – usually within 15 working days, prior appointment required but not needed with payment of additional $75 walk in fee (accepted on first-come first-serve basis).