We tried exactly the same thing....
Limited number of keepers....contract limited to three years.....on an escalating pay scale.
Sure, it happened where a player got too expensive to keep but the franchise would just substitute a cheaper player that year and that was a player that was untouchable for everyone else.
It looked good on paper but the bottom line was that you KNEW at the beginning of the auction....just like a draft.... there were players that you had absolutely NO CHANCE of obtaining
...only it was worse.
We have a 14-team league so if I was picking 14th in a draft, there were 13 players that I KNEW that I had no chance to get.
Although I didn't know exactly who those 13 players were going to be....I could probably guess at least ten of them.
When we implemented the "3 keeper max" rule....there were up to THIRTY NINE players that I didn't have a chance to get.
Although I could keep three players myself...it simply wasn't worth the price and it totally killed the concept of the "get any player you want" auction format.
Not only that...but the increase in the "level of strategy" that you said increases is also just another level of "luck" when a backup RB that you got for $1 in year 1 gets traded to a team where he becomes a starter during the off-season and his value increases.
This wasn't strategy, it was an unforeseen circumstance that a franchise benefits from through no foresight on their behalf.
The strategy in an auction format comes from everyone bidding on a player under the same circumstances.
I highly recommend that you drop the keepers and keep the auction format pure...."if you want a player...bid another buck"
After all....that was the reason that you switched to the auction format in the first place...wasn't it?
We were coming from a straight redraft/serpentine setup and had discussed both Keeper and Auction options for several years. We didn't have one specific reason we changed from our previous format. Some people didn't like the luck involved in the drafts (one guy consistently got 11th pick several years running), some wanted the keeper aspect so they could have more than 1 year of investment in certain talents, and others were drawn to the "if you want him, you can get him" aspect of the auction format. Every motivator we had for change had multiple options to address them, but we happened to choose a system that hit each of them to some degree or another.
This system has worked out well for us, and we've already gone through at least one cycle of "max contract" guys, and the influx of talent that came with those guys being available for auction again. Every year a month or 2 prior to the draft, we put the option for adjustments on the table, and nearly everyone has consistently said they enjoy this setup and wouldn't want to change anything. Sure, some luck is involved in undervalued guys, but the same is true for any other format that involves keepers. We mitigate the "dumb luck" by having minimum keeper costs of $10/15/20 each year, so that $1/waiver RB who benefits from 2 injuries in front of him doesn't completely blow up the economy. It still rewards someone who does their homework on rookies, depth charts, and contracts, to anticipate opportunities that players will have in coming years, allowing someone to take advantage of low current value that turns into big future value. You have to take the good (strategy/planning) with the bad (outright luck).
And if you really want a certain player, we do allow trades (like nearly any other league) so you can go out and "buy" someone you specifically want, as long as you are willing to move equivalent talent from your team
If our only (or even primary) motivation for including the auction system in our league was to guarantee that an individual could buy any player they wanted, then we wouldn't have considered the keeper option...since, as you clearly point out, Team 1 keeping someone clearly means Team 2 can't "buy him at whatever cost." That wasn't really an issue for us, since we had more than that motivating us to switch our system, and we settled early on a combination keeper/auction setup.
Ultimately, your league's desired outcome is really what drives how it's set up. Your league just seems to value the "want a player, bid another buck" aspect of the auction more than our 12 owners do. To each their own.