I never did receive any kind of response to my inquiry about the proper procedure of getting my spec script submitted so that it wouldn't just be rejected as unsolicited material, so as I mentioned previously, I decided to adapt it as a fanfic instead.
At least in fanfic form, I'm not restricted to the constraints of a 10 minute and 40something second time limit, so not only was I able to add some material back into it that I previously cut out because of said time limit, I was also able to beef up some of the dialogue and exposition as well.
Some of you here felt like this idea had potentional to work as an actual episode, so let me know what you think of it . . . though, spoiler alert: it kind of/sort of has another one of those "be yourself" morals, just to let everyone know, since many people feel TLH really hammers that moral in too heavily.