Hi,
I've had the problem myself when I started with electronics back then.
I "solved" the issue (or at least make it less critical) by using a simple block of wood which was a little bit narrower than the Chip itself. I placed the chip up side down on the table, inserted the wood between the rows of pins, and then used to other pieces of wood to squeeze the pins to the wood piece from both sides.
I hope it was described clear enough,..
Maybe this ASCII Art gives you a better idea?
| | | NARROW WOOD | | |
WOOD | |______________________| | WOOD
______| | IC LAYING ON TABLE | |_______
You can also easily make a simple 3D design and print it on a 3D printer (or order it from a 3D print manufacturer).
Kind regards
Tony