IC,
I think you'd be wise to talk it through with someone in the Quetico Park office. I believe they'll want to know that you are "making reasonable progress from wherever you enter the park systems to your actual entry point." At least THAT's how that worded to me, sixteen years ago, under similar (but not exactly the same) circumstances. Here is what happened.
I accessed Quetico via Beaverhouse (before Beaverhouse was technically an official part of the park, I believe; anyway, there was/is no permit for "Beaverhouse"). I wanted my actual "entry point" to be Three Mile Lake. The usual way to do that is to hire a local outfitter to run you down to Three Mile via Flanders road (they dump you off at Wisa Lake). I've done it that way before. This particular trip, however, I wanted to camp a couple nights on the west end of Beaverhouse, then paddle down the Quetico and Namakan rivers to Three Mile Lake. So, I asked the folks at the Atikokan Office for a entry permit dated three days later.
They didn't want to let me do it that way. I asked, "How, then, SHOULD I do it?" They huddled up and came back to me with a permit dated for that very day... and then asked me to make "reasonable progress" from Beaverhouse to Three Mile Lake. "Reasonable progress" went undefined, so I said no more about my intent to camp a couple nights on Beaverhouse. Clearly, they did not want me "making waves." Maybe they just wanted "park fees" for those three days. Anyway, they opted to play Sergeant Schultz, seemingly preferring to "know nothing" about what I actually did.
My opinion? While there's a chance this still could be a gray area in park policy, I suspect they'll issue you the permit for the date you want IF you explain your situation. There must be dozens of folks who do this every year (either individually or through outfitters). I've got to believe there's a way to handle it.
Jimbo