SSA 1099. This form includes benefits paid in 2019 for 2019, for 2018 and 2017. Do I put the total on the 2019 return? Or amend prior returns with each distribution?

Income goes on 2019.  A lump-sum election may reduce 2019 tax.  See Lump-Sum Election starting at the very bottom of page 10:

https://www.irs.gov/pub/irs-prior/p915--2019.pdf

I don't know the timing requirements for the election.  It might need to be done on a timely filed return.

Here are your choices for lump sum payments:

When figuring the taxable portion of Social Security benefits, two options are available for lump-sum benefit
payments:
• The first option allows the taxpayer to report the whole payment the year it was received. When the taxpayer chooses this option, complete the Social Security Benefits Worksheet as usual by including the entire lump-sum payment on line 1.
• The second option is to treat the payment as received in the earlier year or years. This is done by figuring whether any part of these benefits is taxable, based on the earlier year’s income. Any part that is taxable is then added to any taxable benefits for the current year and included on Form 1040. The taxpayer can elect this method if it lowers the taxable benefits.