You don’t have to drill holes to mod them balanced (have a look here: The lazy person's *reversible* DT880/600_Ohm balanced mod) but you have to solder some wires - which I consider to be quite easy.
Before you start excessive amp-shopping I really recommend you to test them balanced with a THX 789. For me, they are outstanding this way.
Having told you that, I did some amp shopping myself and got the Beyerdynamic A20 amp for about 200 EUR used here in Germany a few days ago. Merely out of curiosity what the 100 Ohm output impedance might bring out of the DT880/600 and since I heard my Beyer T1 (1st Gen.; 600 Ohm; I also modded that one balanced) with it once and wanted to own it anyway. The T1 is really driven very nicely and be assured that all my high impedance headphones are loud enough on the A20 (100 mW at 600 Ω, 170 mW at 250 Ω and 150 mW at 30 Ω). Of course that does not mean, that they are driven well. The damping factor with this amp really limits the use of lower impedance headphones. The T1 and the A20 are a nearly perfect match, the DT1990 is ok but the DT880/600 sounds “well” but is much more airy, well-defined, controlled, etc. on the THX789. I run both amps of the RME ADI-2 DAC (THX: balanced XLR, A20 RCA). Might not be a fair comparison since the balanced DAC output may give the THX a little bit more swing in its input…
BTW - talking about amp shopping; my 600 Ohm Beyer DTs do not sound great on a RebelAmp I also bought last Month - some other headphones are a heavenly match with the rebel on the other hand).