I did some labs with my PCP before getting into the RE (HMO- needed the referral). My RE didn't make me redo all the tests, but some were incomplete (the PCP sent for FSH/LH without the E2 level..) so I had to redo those and whatever else the PCP hadn't ordered.

I don't think RE's will make you re-do if your testing is very recent. Also, things like day-3 bloodwork is quite standard. I would recommend you do day-3 blood work for AMH, FSH, estradiol, TSH, T3, T4, ATA (anti-thyroid antibodies) at Labcorp using OBG's script. You can also do sperm analysis at a reputed lab like GWU. I agree with your time saving idea. You can also do HSG prior to RE appointment, but might as well wait for it. Let the RE do it with their own x-ray machine etc.
Yes, you can get started! Good luck!

do everything with the RE. they are far more experienced and knowledgeable than regular OBs. and as someone above pointed out, more REs will make you redo the tests.

Your RE will probably make you redo everything. Sperm analysis is the easiest test. My OB have me a script for the HSG. I would NOT jsut go and have it done at a regular radiology place though. Have it done by an RE or someone who does them frequently. Getting the catheter into a full closed cervix shouldn't be done by a regular radiologist.

Bloodwork taken on day 3 of your cycle, HSG for you.

Sperm analysis for DH. DH did that at Shady Grove with a urologist's referral before our first appointment.

DH and me have been trying for 2.5 years and we both are turning 33 next month. We believe it is time to go to RE. It seems like the first appointment with RE is kind of consult, and we may have to wait several weeks for an appointment with some good RE. Regarding to saving time, what tests I can do with my OBGYN? Then I can bring the results with me to see RE for the first time and skip some steps there.