Almaro:
There is no reason why you cannot use the 2250 and the LK 280 together, at least if you use the unbalanced connections on the back of the 2250. Because Linn encourage upgrading through multi-amplification, they make it easier by matching the gain on their amps so that they can be mixed and matched. However, things do change over time, and products change as you go up the chain. So sometimes you have to watch closely.
For example, the LK 280 has a voltage gain of 28.5 dB. If you use the unbalanced connections on the 2250, they have a gain of 28.3 dB. This is not a problem.
However, the balanced connections on the back of the 2250 have a gain of 22.3 dB. This is sufficiently different from the LK 280 that it may be a problem, i.e the drivers connected to the 2250 may sound less loud than the drivers connected to the LK 280, for a given volume setting. It may or may not be a problem. I would suggest sending an e-mail to Linn through their website on this point. They're pretty good in answering questions about their products, although it may take a few days for a response.
So, I see no problem using the unbalanced connections, but the balanced connections might be. See what Linn has to say.
The reason I suggested the LK 85, LK140, 2250, AV 5125, or even the Majik, is that they all have internal Aktiv card slots that will fit the old style Aktiv cards, i.e. the pre-Chakra cards. I do not think that any of the other Linn amps, such as the LK 280 have an internal Aktiv card slot. This means that if you wanted to go Aktiv, you would have to purchase a Tunebox to hold the Aktiv cards, which is an additional expense, on top of the additional cabling required.
Thus, you can passively biamp using the LK 280 and 2250 right now. However, Aktiv biamping would require a Tunebox as well as the Aktiv cards.
By the way, Linn recommend that when you biamp, the better amp should run the tweeters. In your case, use the 2250 for the tweeters and the LK 280 for the mid/bass drivers, although you can certainly switch them around and experiment.
When I went to passive biamplification, I noticed some improvements. First of all, the amps ran a bit cooler since each amp was only powering one set of drivers. I also noticed a slight increase in background detail and better dynamics. However, I did not find the change to be huge and I wondered whether it was worth the extra amplifer cost. On the other hand, when I went to Aktiv, the difference was huge. So you should not judge what you will get in Aktiv biamplification based upon what you get with passive biampflication. I think that passive should just be an intermediary step (probably for budgetary reasons) on the road to Aktiv, rather than a final destination in its own right.