No but if you understand why you are losing the quotes (and this should be done on the follow up call) then if it' is an accreditation thing you have the ammo to look @ accreditation. More than likeley the seller form the accredited co will be bigging up accreditation (as they should I suppose if they are paying for it)
I have just had my screen replaced on my HP Spectra, cracking machine (literally), it's 18 months old roughly and a known issue with the hinges causing the problem but HP still wanted £300 to replace.
Your checks are commendable but too comprehensive imo, I'd expect those on a monitored takeover.
Discuss the history of any issues, check bells, batteries (Inc current and charge) , induced ac at a push, walk test Inc pa's, cct resistance, brew.