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I think the short answer to your question is that CBA has provisions that if the CBA is not extended, the salary cap rules change. And those rules don't allow you to do what you are saying. For example:
The 30% rule: The CBA, if not extended, imposes a rule on how much a player's salary can increase or decrease from one year to the next. Your non-signing bonus salary cannot change from one year to the next by more than 30% of what you were paid in the final capped year (2009). You can see that part of the CBA
here, scroll down to page 133 and look at Section 8: 30% rules.
Just that rule already makes your example impossible. To have a 7 year contract with $55m in salary requires a minimum of a $4.1m 2009 salary, but would pay $24m over the first 4 years of the contract instead of the $15m you wanted to pay. You can try to get fancier, pay $5.4m in 2009 and then pay the min you can in 2010 and 2011 and then start increasing again, but to pay exactly $15m in the first 4 years you can only get those late salaries up to a total of $36m... and they may not be high enough the player will agree to pad on the extra years since some of them are reasonable salaries you might keep him at.
Signing Bonus Proration rule changes
It used to be that teams could prorate signing bonuses over 6 years. With the CBA not having been extended, that drops to 5 years. So even though you're talking about tacking on 3 more years, that really doesn't help you that much in spreading out the cap bonus. It doesn't help any more than making it a 5 year contract would.
Though one thing I'm not clear on is what exactly it means having to prorate a cap bonus into a year if the year is uncapped. I've seen some people on the net say some things about all prorations suddenly hit you in 2009 but that doesn't seem to be the case from what we see in contracts. So I'm guessing here, but I think the NFL is figuring they will get a new CBA and there will be a cap and you don't want to screw yourself by having too much money prorated in the hopes there is no cap when it hits so it doesn't matter. But that's a guess.