Tips for optimizing through-hole soldering
Decades ago there were clamping systems available. Components were mounted on the top side, a sheet of board-backed foam pressed down on the stuffed board and a frame clamped the whole lot together prior to turning upside down.

Figure 1. A solution from Nuts and Volts.
As usual, you'll probably need to do the low-profile components in the first pass and the taller ones in subsequent passes.
Check the linked article where a design is published.