First (OT-ish) suggestion: I'd drive coast-to-coast west to east. Having done this both ways already, you will find driving into the afternoon sun a bit tiresome after a week or so. Route 66 LA to Chicago is particularly worth trying - lots of historic sections and plenty of dedicated services.

Flying-wise - do you have a BA Amex card? If not, get one, spend £10K and use the 2-4-1 voucher to double the value of your miles. 150k will then buy you two returns in F.

Alternatively, you could buy one CW return for 100k, the other as an MFU WT+ plus 25k miles, leaving you 25k in change.

Oh, and welcome to FT!