First of all, do not wait to have the tests. They encourage people to get as many done as soon as possible. Certain things like an SHG/SIS, Mammogram and pap as well as the psych consult and your partners's SA are big things that you can get done now. You will not be able to gain access into the donor base until all requirements are completed. I had almost everything done by the time I had my consult and I had many more things that were required because I am 45. I only had to complete a few more blood tests for me and my DH and the Dr. was very happy about that. They might order RPL or a thrombophilia blood clotting panel of tests for you. Your Dr. might also suggest a endometrial scratch biopsy. That being said, additional testing should not prevent you from getting out the way all that you can now.
I am an out of town patient. I had my scratch endometrial biopsy (optional in most cases) done by my Dr here and will be monitored here by my Dr. The monitoring is minimal. They only require one lining check during the cycle if all looks well. Betas and post pregnancy tests and such can all be done here. When you go to RBA for your "Thaw date" they also set you up as an out of town patient to do your mock transfer then and meet with your physician on the same date. How long you will have to be in Atlanta depends upon whether you ship frozen sperm in advance and whether you have a three or five day transfer. We are using my husbands fresh sample so I have to be there for 6-7 days. If you give a sample in advance, you only have to be there the day before a possible day 3 transfer. You will not know whether it will be a 3 or 5 day transfer until Day 3 so you have to plan on staying until at least day 5. Most seem to have Day 5 transfers but some do have a day 3 transfer. So, if you are pressed for time, ship frozen and go down for one day in advance to meet with your Dr and have a mock transfer/sounding. BTW..what is an HSG cycle? Do you mean a cycle with stims?
FYI, you might want to check out this link which has a huge RBA thread. If you study it, you will learn a lot about how things work there. Good luck.