Quadrantal levels are only required above the transition altitude, and also only outside controlled aispace. So you can fly across the EGNT CTR at any level you choose, with the appropriate clearance from ATC.
I'd have been tempted to read the alt corresponding to FL45 off the second alt (set to EGNT QNH) and ask to transit at that level. If refused, the solution is straightforward -- do what ATC says!