Excellent play. I have the Golden Gate 3 and have no interest in a preamp.
Some things to consider with the Big 7 vs the GG:
1. Both use DHT tubes that will give you a big, wonderful, engaging sound.
2. Do either of the amps have engine 11? That is Lampizator's latest upgrade and it is worth the difference if available. Alternatively, Lampizator will generally install the upgrade later but it isn't cheap. However, engine 11 isn't a deal breaker, without it the DACs will sound better than most, as Gary Koch famously called.
3. Single ended vs balanced. I prefer single ended and you should too. The SE amp uses 2 output tubes vs 4 for the balanced. I think lampizator built the balanced just because there are fans of the balanced system. I don't consider it an upgrade. While the output tubes will likely last forever in the preamp position, having only 2 output tubes will make tube rollling much less expensive.
4. Many newer Lampizators have an analog input which is handy if you are using your DAC for a preap and you want to add an analog source, such as a phono (you'll need a phono pre or a SUT) or tape deck. You can also run your HT front speaker pre-out through it for watching movies if you have an HT system overlaid on your 2 channel system. so check if either of the DACs you are looking at have this feature.
5. The DAC is the heart of your system so I agree with putting money into a good DAC. You've already gotten some advice about your amp.
Jerry