You may want to try to get in person fit advise but I'm not sure you should sell just yet based on your pics sitting on the bike or buy a stem just yet. The important thing is to avoid bike fit hell by self fitting, but if you want to try, mark baseline for everything with a sharpie or tape and start going for rides and moving 1 thing at a time. You look to be a tad high on the seat as-is from what I can tell, it is better to be slightly low than too high--especially if you have back issues, the higher you are, the more you will recruit back muscles into your pedaling, those should be used for stabilizing. Mark baseline with a sharpie, and move the seat back and down 3 mm at a time, go for a ride (10-20 miles) and write down your observations such as sliding forward/aft on the saddle, knee/back comfort, ease of spinning and flat and hill power, wrist comfort etc, eventually you'll find where you should be for the saddle based on how you peddle, for a single speed, knee generally ends up a little aft of spindle, you'll get more power at the expense of cadence there and the more weight over the back wheel, the less on the hands, work on rotating at the pelvis as other have said.

Once you get seat dialed in, you then worry about setting your bar position. First you find reach and stem height as well as bar rotation for comfort in the drops. You should be able to ride in the drops for 30 minutes with relative comfort, if you can't do that once your saddle is dialed in, then start looking at stems. One you get saddle and drops set, you then set the brake hoods, ride for a while, and then once your confident, wrap.

It's going to be a PITA to try to swap stems with quills because of all the work to remove quills that don't have removable face plates, but a nitto technomatic with 100 mm reach is probably a safe starting point.