Most gigabit Ethernet boards worth anything support TCP checksum offload and also support jumbo frames and interrupt coalescing and have generally better bus interfaces than many low end 10/100 chips (there are good 10/100 chips out there, but your $5 NICs aren't using them!). An Intel Pro/1000MT is $41 from Newegg and has these features and good performance. And if you have reasonably recent PCs, you can get two gig boards and get >100Mb/s TCP performance. (two of the Intel boards are cheap enough, at $82 total, and just connect them with a normal STRAIGHT Ethernet cable -- 1000BaseT is auto-crossover and a 10/100 crossover cable that doesn't cross the unused pairs won't work right) Avoid the really cheap gig boards based on the Nat. Semi. chip.
TCP does introduce some extra overhead, yes. But modern OSs are heavily optimized for TCP common case performance to the point where "lower overhead" protocols may in fact run slower in practice. If your application is to just use the other disks as offline or warm storage and copy things back and forth, TCP has the right qualities for you. If you want to use them as a real filesystem, then TCP might not be the right answer -- but if you're running Windows (which I'm assuming), then remote filesystem performance is just never gonna be very good anyway.
Why don't you get a two-drive external Firewire IDE (I'm assuming you're using IDE) enclosure and a Firewire adapter and use that for some drives? It would sure seem to me that it's likely to be a lot faster, you get the convenience of a local disk (though a bit slower than direct IDE), and not all too expensive a move (maybe $100 total?). Or why not get a serial ATA adapter with the PATA<->SATA dongles (I think Promise makes a 4-port ATA RAID with 4 dongle retail kit that's like $120 at Newegg) and run the SATA cables to an external enclosure (it'll be kinda a kluge, but best performance of all and again not too expensive). If the problem you're really trying to solve is to get these disks outside your case but otherwise you really want to use them on your main PC, you should probably be using a disk-oriented solution and not a networking solution, as you'll get better performance for your $$ investment.