Syphilis Treatment question for HIV positive male

I was diagnosed being HIV + in 2016 and began treatment shortly after diagnosis. Transmission occurred most likely in 2013. VL has been undetectable for every test since and CD4 was 900 last test. After establishing care with ID doctor, I also tested positive for Syphilis. Titer at time of diagnosis was 1:256. Doctor gave me 2 shots of penicillin at same time. Titer dropped to 1:64 a few months later. Then it jumped up to 1:128 but lab most likely made an error bc upon retest a few days later it was 1:64. Fast forward over the years and the Titer stayed the same until 2021 it went down to 1:4. 6 months later, it is now 1:16. I believe that it is a lab error in dilution assay but asked doctor to prescribe me doxycycline 100mgx2 day for 14 days. One day before starting doxycycline, I took 3g of Azithromycin out of fear. My questions are this: 1.) Is it possible that the Titer decrease to 1:4 was an error as I had never been below 1:64 prior to that? I understand that a four fold decrease indicates positive treatment success but also a four fold increase indicates possible reinfection. 2.) is it possible that the 1:16 titer is in error if the 1:4 is valid? 3.) I have access to a large quantity of Azithromycin not expired or old. I find no drug interactions between doxycycline and Azithromycin so will it help eradicate the infection if I give a two combo punch similar to a two-three drug regimen that is available for HIV? Going to take doxycycline 200mg/total a day split into two doses and since I took 3g of Azithromycin already was going to take 500mg a day for 15 days. I just want to make sure I won’t be doing more harm than good. I don’t care about any possible liver damage or kidney problems bc short term goal is to get rid of this disease. I would like to point out that I have had zero symptoms that would indicate to me that I had reinfection. No chancre, no sore, no rash, no headaches, back pain, hearing loss, spots on soles of hands or feet, nothing. Also, sexual activity has been very restricted, lower risk and very infrequent. Thank you In advance for your reply.