Schengen visa questions

[imi_user08]

I am going to apply for Schengen visa at German consulate in Los Angeles. From their website, they require a proof of medical insurance with coverage of at least $37500. I'm GC holder. I've medical insurance from UHC thru my employer. UHC rep said that they cover medical emergencies outside of US and will be sending a letter stating my coverage limits including out-of-network coverages, but won't be able to mention $37500 amount that the consulate is asking for.
Is there any need to buy additional insurance? Has anyone experienced any visa rejection due to lack of additional medical coverage?
I'm going to carry following docs when I appear in person:
- Original GC, Passport
- Employment verification letter
- Bank statements
- Letter from UHC for medical coverage
- Printout of E-ticket showing itinerary
- Letter from escorted tour company who is arranging my hotel stay.

Is there anything I am missing?

I'm going to apply for multiple entry UK visa as well. Is it possible to get both visas the same day since the German and UK consulates are clsoe by? Or do I have go there on separate days? Do both consulates accept cashier's checks in USD?

Appreciate your feedback.

[visahlp]

hi,
these are the required documents for you:
* Valid passport (an additional copy) with at least 6 months validity remaining
* Fully completed application form
* 2 passport type photographs (no older than 6 months)
* Valid US alien registration card or valid US resident Visa and one copy
* Current bank statement and one copy
* Proof of health insurance coverage for trips outside the US and one copy
* Proof of group travel/hotel reservation/airline reservation and one copy