"My view is that a draw is always a seven way loss. I realize others put a lot of value into draws but I don't."
Yes, great sentiment but still a flawed solution.
Let me show you some examples:
In this game: http://webdiplomacy.net/map.php?
gameID=168928&turn=13
Germany is clearly in the lead and only getting stronger. Under your premise everybody most likely just drops what they're doing and stalemates but not necessarily the case under a regular situation because perhaps Russia is worried he'll get downsized or maybe Turkey and Italy think they can force a 3WD if they let things go on long enough for England and Russia to get eliminated and Russia and Turkey can't get along.
Or in this game: http://webdiplomacy.net/map.php?
gameID=160111&largemap=on&turn=9
The only chance this has of going onto a solo is if Italy, knowing he's being pushed out decides to king-make, under 'everybody gets a participation award' mentality this game stalemates in a couple turns.
In this game: http://webdiplomacy.net/map.php?
gameID=80849&largemap=on&turn=12
The solo opportunity presented itself only because Turkey and Russia both knew if there was to be a draw they needed to step on each others heads to keep their spot in it causing enough instability for a solo to occur.
This game http://webdiplomacy.net/map.php?
gameID=67632&largemap=on&turn=19 was soloed because the writing was on the wall for France so didn't bother even defending Munich. Had he just bounced Munich, despite still being eliminated the next year the rest could have taken Tunis back and stalemated. He'd get the shared win anyways, but since that wasn't an option he didn't care.
So there's a lot of solo paths here you cut off by introducing this, far as i can tell you start limiting your solos to either games where two players are completely equally matched and race for the finish line or scenarios where the player times his final stab so perfectly and so out of nowhere that it's too late to do anything about it. Both fine respectable finishes, but for what you lose i don't see what you gain in this? Maybe more people try for solos but the climb is now harder for them to get there. You're encouraging stalematers just as much as you're motivating solo seekers. The game would be much more interesting if the solution involved a means to keep everybody invested in seeing the game carry on as long as possible, that's when solo opportunities open up and that's when the competitive juices really come out. I love me a good heated end-game.