I expect he will have two motors

, besides there is slightly more to it then that...
Just a thought, but will you really need all that sheet for the 50$ 'bot. I would have thought a 10 x 20cm base would be plenty. Weight comes down to ~500g for the base, and you can make four 'bots form your sheet...
And if the wheels are that heavy there is a good chance they are far stronger than they need to be. You could probably lose some mass by drilling holes in the wheels and the base of your 'bot (but save that as a last resort because it is hard to put back...).