If you have that much vertical height, the "L" part of inverted L really would do nothing good for you. Just put up the vertical element. If you want it to work on 40 limit the vertical height to 80 feet, that would be a 5/8 wave for 40 meters. For 80 & 160, 125 feet or so would be pretty close to 1/2 wave / 1/4 wave, which may be good or bad - the end impedance of a 1/2 wave is very high so hard to tune. I have seen an antenna feedpoint matching system for a dual band 20/40 vertical, which properly tunes each band to the respective 1/2 wave or 1/4 wave impedances, so that presumably could be scaled to 160 & 80.
If you're going to use a remote tuner anyway, something to consider would be a length of 105 feet. That would get you away from the 1/2 wave end impedance on 80, and would be a 5/8 wave for 60 meters. With the europeans getting 60m allocations, that would kick butt at transatlantic contacts.
Using the N6LF ground radial dimensions I would probably put out 8 radials for 80m and 4 or 8 for 160. And 4 for 60 if you do the 105' height.