You know, I wouldn't normally give this sort of advice. But here it is.
If you're already working within an MBB firm, helping the partners reduce their tax bills, then you have a golden opportunity to build some relationships. You are already on the payroll, what you want now is an internal transfer. Despite what many might say, Partners do have a LOT of discretion... so if one of them wants to put you on a team and utterly bypass the HR and recruitment processes, it WILL happen... despite what HR might say. Maybe you could get onto a team in a back-office sort of way... just providing a bit of support from the office and some analysis, possibly in addition to the tax stuff... like the partner is temporarily reassinging you for a bit.. then the next step would be to do the same on another project.. then another... then get a bit more involved with other things on the team too... then next thing you know, you've become a consultant by stealth and with the blessing of a partner who trusts you enough to want you on his teams...
Easier said that done, I know (especially when you're working with a firm full of Harvard MBAs and so on), but you are already in a special position here and I would say a bit of wheeling and dealing of this type is your best bet.
Also, you say "I have recently moved to the inhouse Partner tax team at one of the MBB firms". Do they really employ a TEAM of people just to deal with their tax! Wowser.