One thing to keep in mind (and I assume you have) is that BA requires 4 BA-metal segments per status tier bump; i.e. 4 from Bronze to Silver, 4 more from Silver to Gold.

Owing to BA's fuel fines (again, probably something you know about) RTWs aimed at harvesting umpteen tier points - combined with the 4-segment/tier requirement - can make for awkward and expensive RTWs. That is, using BA for your first flight (e.g. BUD-LHR) will open the door to high fuel fines throughout the ticket, whereas using some other carrier for first flight and/or ticket issuance (e.g. RJ AMM-JFK) will be cheaper, but will mean that getting the 4 BA segments done within the bounds of the RTW will be more complicated.

So I'd probably be looking at some rapid mileage runs on BA metal prior to commencing the RTW if the 4-segment rule with BAEC is an issue. Then if you're going up a tier during the RTW, end it with some BA segments and/or with BA repositioning flights after the RTW is over. The BA flights prior to/after the DONEx wouldn't have to be in business class - a couple of rapid LHR-AMS/CDG etc. turns in economy would do - thus conserving RTW segments for longer hauls and avoiding BA's fuel surcharges in the process.

Hope that makes sense.