It's hard to know what will happen, to be honest.
In regards to the information you've been given, I wouldn't actually rely on any of them to give you accurate information - the only people who would be able to tell you whether you can travel or not are Sheffield/the UK government themselves.
- The majority of lawyers we've come across here have given bad advice and haven't known the rules anyway
- the £1.37/min helpline is notorious for giving incorrect information and bad advice (including advising people to apply for visas they didn't qualify for), so I wouldn't believe a word they say
- VFS Global are really just a commercial company and have nothing to do with UK immigration rules, so I wouldn't be surprised if they didn't know and are just assuming. In fact, they provide services for people applying for visas to many different countries and so are unlikely to keep up completely with the immigration rules of each country people are applying for visas for.
I'm curious... Which countries did you see that list the 'Keep my Passport' service whist advising against travel to the UK? Until about a month ago, I suppose 'Keep my Passport' wasn't even an option for US applicants.
I just wish we weren't in the first batch of people attempting this 
I checked a few different countries on VFS Global:
- several didn't offer the 'Keep My Passport' service at all (Argentina, Chile, Bolivia etc.)
- some offer it but don't mention anything about reasons you might keep it (i.e. India)
- Hong Kong, Saudi Arabia and Pakistan said you could keep your passport for travel to countries other than to the UK
- Brazil and Canada said you could keep your passport for 'travel' (no specific mention of the UK) or for applying for a visa for another country at the same time
The TLS website is down at the moment, so I can't check what it says for the countries serviced by TLS instead of VFS Global.