So the stains were present WHEN you moved in, and haven't gotten worse? If that's the case, it may be prudent to see what you can do to remove them.

If you are not adding copper, and are not getting new copper stains . . . you don't need a copper test. In any case, a copper test is not going to reliable, because you probably still have HEDP in the water.
  • Getting a salt test is also optional. If you'd like one, that's fine. But it's not going to be essential, or help you remove the stains.
  • Getting a K2006 is necessary, because (a) you need to get away from pool store tests, & (b) you need to be able to test your CYA levels, and accurately test your chlorine levels.
  • Getting borate strips would be helpful, because dropping your carbonate alkalinity (baking soda) and replacing it with high CYA (per Pentair) and high borates make your pool less conducive to staining.
  • You will need to maintain calcium levels, to protect your plaster.

But, a pH of 7.6 is not going to corrode your heater.

So, for now, keep your pH on the low end of the scale; avoid adding bicarb; get a K2006; get borate strips if it doesn't push your budget; and continue to use HEDP per the bottle label.

By the way, if you are considering acid washing, simply draining, treating the stains directly, and then pressure washing may be more than enough . . . and not nearly so hard on your pool.