I'm flying LHR-XXX Friday on an M fare. Upgrade to new biz is 20K miles +$250. I have 0 miles

Three questions :-

1.) if I buy the 20K miles, what are the chances they post in time for check in?

2.) Can I pay the $250 at online check in? (the reason I ask is that the parental visa is coming into play, which won't be there if I do check in at LHR.)

3.) Is a paid upgrade on the day going to be more or less than the $930 total the miles+co-pay totals?

Or, do I submit to the indignity of a $97 E+ window seat?