A lot of sources of calcium will have a liming affect on your soil. Be aware of which ones will raise your soil ph and be conscious about how much you add as it’s easy to overdo it. Certain calcium sources will have more of a liming affect than others. It’s a lot easier to raise soil ph than it is to lower it, so I would advise not letting your soil get higher than 6.5 ph unless you want to add sulfur to your soil (gypsum already does this).
Gypsum is a neutral calcium source as you mentioned. You can find it micronized which allows it to be suspended in water and fed by irrigation (or hand watering or however you do it).
This will give you one of the fastest doses of calcium that likely won’t impact your soil ph. That being said, as the calcium breaks free from the sulfur and is up-taken by the plant, the sulfur will likely have a minor acidifying affect until up-taken or leached from the soil.
Since you are on the lower end of where I would feel comfortable ph-wise, you could add just a little bit of Oyster Shell Flour or Bonemeal until you reach maybe 6.3 ph. Then use Gypsum to reach your target Calcium soil ppms or meq, or base cation saturation ratio or however the lab is giving you your results. The slight amount of liming from the OSF or BM will help buffer any potential acidifying action from the gypsum as I’d assume you be using significantly more gypsum than other calcium sources based on what you’ve told us.
One thing to keep in mind is that gypsum can push a lot of other minerals off their bond sites in soil. That’s great for your overabundance of potassium, magnesium and phosphorus (phosphorus, as an anion, will leach away with waterings naturally).
Too much potassium in the soil can be a pain and compete with Calcium uptake, same with Magnesium.
This is regarding field crops but I think is still a safe range to fall into. My soil is pretty damn close to this ‘ideal’ range and plants are banging.