At first I was thinking about adding new floor decking on the top floor making sure that it was perpendicular to the old decking, but that is not good, because you do not need the extra weight.
Then I thought about using the criss cross's under the floor that has been used many years on older homes, but that is mainly for 2 x 6's and 2 x 8's. I do not think that this would assist you with those 2 x 4's.
Then I thought about scabbing addtional 2 x 4 alongside the old 2 x 4's. This will give you some relief and not add too much additional weight. I would use this one and see.
Now, when attaching this new 2 x 4 I would make sure it is perfectly straight and preferably not pine. Use a hardwood that is strong. I hope that you have room for this operation, but you want to screw the new 2 x 4 to the old. I would screw a set of screws every 6 to 8 inches and have one close to the top and one close to the bottom. Do not get so close that the board will crack.
You might even consider renting a floor jack or using your sissor car jack and pushing up alittle to make the new 2 x 4 up against the floor tighter. Not too much pressure as to damage the first floor flooring. Or not too much to bow the second floor, Just snug it up. Then hit the screw gun. Do not use drywall screws. use a good heavy 2 1/2 inch deck screw. You might want to use the heads that are allen heads or hex heads so that you do not strip the phillips heads.
This will be a two person job and a slow one, but I think that you can make some difference.
also, if you use the jack, you might add some shims under the old 2 x 4's to make up the difference. Let me know your thinking.
I will stay tuned to your entry for other good advice. I would like to hear of others opinions also.