Hi Ralph,
Using an IP redirect to serve country-specific content to the user is fine (i.e. it isn't considered to be cloaking as your intent isn't manipulative). However, there are issues with doing so - as you've highlighted - you're also redirecting the bots so have seen the UK site suffer.
Because of these issues I don't normally recommend the IP redirect approach. I also think that it can be bad for users too - just because someone is in the UK right now - doesn't necessarily mean that they want to see UK content - e.g. they may just be here temporarily on holiday / on business etc.
Personally I would prefer the javascript overlay (your option two) which allows users to pick the relevant country rather than implementing a hard redirect. This will also allow the bots to index both versions of your site.
I do understand the ecommerce team's concerns over this increasing bounce rate - but I'd suggest that if it's implemented well - check out amazon.co.uk from the US - this shouldn't cause you problems with bounce rate.
Likewise I understand their concerns re US / UK customers seeing the wrong content and therefore exposing the price differences - however, again I'd suggest that it's probably more important to have both versions of the site indexed.
I hope this helps,
Hannah