Again, only having heard the Senns and not the SE's, and not being a classical taper, I wouldn't want to venture too far afield of what I'm talking about. But in your price range, a mic with a much more neutral tone, to my ear, would be the Milab VM-44 Links. For a bit more money, I think the DPA 40xx series of mics have an extremely neutral and natural response that is ideal for recording in good-sounding rooms. If you keep an eye out, you might be able to find some DPA 4011s or Schoeps MK4s used for about what you were looking to pay for the Senns new.
Do you require a "low profile" or is a full-size mic acceptable? Obviously one advantage of the Senns is they are nice and compact. The same is true of Milabs.
DPA's 402x line, which is discontinued, is even lower profile and has the same sonic signature as their larger mics. You can probably find a used set in excellent condition for $2400 (price of new 8040s) or less.