Unfortunately console mode isn't an option for me anymore as I cannot full screen it and playing in a 2X3 inch window isn't viable... (I hate windows 8.1)
I'm not that familiar with Windows 8, but when I'm making my recordings in Windows XP, (and it won't let me record in fullscreen) I lower the overall resolution to make the window take more space on the screen and I also increase the font size of the window. In XP, I can do that by right-click -> properties on the shortcut or on the window itself. (I suspect there's a way to do that in Win 8 as well; you might need to Google it) I'm able to get it to take up most of the screen, which takes a little bit of getting used to when I'm used to fullscreen, but it's very playable.
Regardless, there are other ways to increase the speed through the Config.lua file: turn down the "rundelay" to 1 or even zero. (By default, the game puts realtime delays in the "run" command) Also, turn off the bloodslide effect. (It speeds things up between levels) These things won't give you a lot of extra time, but every little bit helps. :)
That covers the technical side of things... next, strategy...
You're obviously quite proficient at the game, as evidenced by your
recent mortem in which you nearly got a YAAM conqueror at HMP. (Awesome!) :) I'm with you in the camp of being a player who tends to play slowly and ploddingly; I take time to consider every move, especially when things get difficult, so I know it can be hard to make that switch to playing fast and not overthinking things.
May I ask what's your most common way of failing at this challenge? Do you get killed or do you just run out of time? If the former, I suggest you slow down and breathe a little; for ITYTD, 30 minutes is more time than you might think. If the latter, then I'd say you're spending far too much time on individual levels when you should be heading straight (or straighter) to the exit. This is not a challenge where you're going for 100% kills. You just need to find the right balance that works for you.
Beyond that, build suggestions: Scout is the obvious choice for the stair sense, and as others have suggested, melee saves quite a bit of time too; just walk into your enemies instead of mashing of F and R. (I've had quite a bit of success in speed runs with a Blademaster build) I recommend you do a stair-dive to Chained Court, grab the chainsaw, and make the berserk last as long as possible. Just go straight to the exit every time, only killing enemies in your way and don't deviate from your straight line to the exit except for particularly tempting prizes like more berserk packs and/or invulnerability spheres. Like I said in the above paragraph, how much you do deviate depends on your playstyle and where you fall on that balance between going fast and thinking (overthinking?) about things. You might need to experiment a little to figure out what works best for you.
Good luck! I'm curious to hear about your results! :)