Yes. I agree with FPM. If it's a matter of logistics, just grind it out man. You don't want to miss out on a R1 deadline.
Here's what I'd do. Upload the incomplete transcript for now. Email them that there was a mix up with your transcript (use more business-y language if you have to, but I wouldn't)
Tell them that you're actually committed to make ends meet and take the trek to your college to pick it up. That way they will have a record if you get it later than you have to for you to be able to send it in later in case you miss your deadline.
The fact that you are super willing to do what it takes will offset the fact that you lost your transcript.
And about them dinging you because you made a simple request? NO WAY! If you're someone HBS was willing to admit, you definitely have way too many good things going for you for one small goof-up to undo anything.