There are ways to shorten the games without meddling with death timers or towers. That combination makes the loss of a team fight an absolute game ender for the losing party, and a comeback is next to unfeasible.
What WOULD increase game speed would be to simply increase how much gold you get, or add a softer way to get gold. Getting gold faster would mean getting to full builds faster and would mean that the laning phase would end sooner. Once that's out of the way, then there's the Team Fight phase, which is the real meat and potatoes of the game. A way to "softly" earn gold is similar to what was done in Infinite Crisis (rest in peace). In that game, if you didn't directly last hit a minion, that minion dropped a small coin that gave you a fraction of it's kill gold, which meant you didn't get totally starved if you couldn't last hit; Furthermore, if an ally last hit a minion or killed an opponent near you, you also got a fraction of that kill gold as well, which helped to keep duo lanes adequately equipped and kept support characters in the running and not having to rely so hard on gold income items just to scrape themselves off the pavement. Things such as this would speed the game along without punishing losing players and without weakening towers to the point where they're nothing more than very large minions.
Speaking of towers, another thing Infinite Crisis did to speed the game along was allow you to access the shop while you were within the range of towers. This meant you actually had more time in the lane and spend less time recalling every single time you needed to buy stuff. Something like this, or even a shop that appears halfway down the map once the game hits a certain time mark would go quite a ways to helping game time go a little quicker. To compare, games in Infinite Crisis topped at 20-25 minutes against AI, and only 30-35 against humans.