I doubt you are going to find an Ayre K-1 with a remote and the phono section for $2K, (typically, the base K-1 with phono and remote would go for around $3K), but you might be able to find an old K-3X with a phono section for that amount. (The K-3 is very similar to the K-1, but it only has two sets of balanced inputs and two sets of single ended inputs, (versus 3 and 3 for the K-1). And while it has two sets of outputs, it has one set of balanced outputs and one set of single ended outputs, and I don't think that you can use them at the same time.
The phono section is very good, (great at this price point!), but realize that Ayre believes, (as do I), that one should use balanced cables for cartridges, so the phono inputs are set for XLRs, not RCAs. This means either having your cables terminated with XLRs, (which I have done), or using XLR-RCA adapters, (as I used to do before I upgraded my tonearm). The phono section does allow you to adjust both the gain and the loading via changing resistors. (Doing this is relatively easy, as it does not require soldering, only the use of screwdrivers.)
Good Luck in your search!!!
The phono section is very good, (great at this price point!), but realize that Ayre believes, (as do I), that one should use balanced cables for cartridges, so the phono inputs are set for XLRs, not RCAs. This means either having your cables terminated with XLRs, (which I have done), or using XLR-RCA adapters, (as I used to do before I upgraded my tonearm). The phono section does allow you to adjust both the gain and the loading via changing resistors. (Doing this is relatively easy, as it does not require soldering, only the use of screwdrivers.)
Good Luck in your search!!!