Snowman,
Way Phat video you made, I like the pop-up comments.
Over the years I have found at least one practical use for high school math and physics - I built my own computer program for torque/horsepower and et/mph. So I applied my "DeuceCoupe Gonkulator" to your car, and your dad's Stage 1.
The Car Life road test of a 1968 400-T400 Stage 1 shows
14.40 at 93.0mph
My Gonkulator computed
14.80 at 92.2 on its first try, and
14.47 at 92.6 after upping traction a bit.
About the only practical change that helped was a modern 2-1/4 Flowmaster or SuperTurbo exhaust, computed to
14.30 at 94.0
So, if your dad runs a well tuned stock Stage 1, that is what you'll be up against. Can it be done?

Well, nobody road tested a Special 250-3spd that I know of, but the Gonkulator computer said you will run:
18.38 at 72.3mph
If the engine is in good shape I'd suggest taking it to the strip and try it. You'll never get that bone stock data again.

I swapped in a T5 and 4.10 posi for a computed
18.05 at 74.4
That is actually a big improevement, but there is so far to go.
Note, I've not done a T5 swap (yet) but per your questions above, if you can, hit the yard and get everything from flywheel and bellhousing through the driveshaft. A good yard will make a nice deal on all that stuff, then you have it all.

Well back to the story. Your 6cyl now finishes the 1/4 mile about 400 feet behind your dad's car. It would be hard to tell a Skylark from a Chevelle at that distance. What to do?

If you're following Tom Lowe's 250 dyno test series in the long thread below, Tom's first step is a stock 250, plus 4v, plus headers. I did this to your computer car and Gonkulated:
Stock 68 Special, 250-T5
Single 3" exhaust or dual 2-1/4"
250+4v+headers
16.51 at 82.0mph
That will feel like a whole new car and will now give some 289 Mustangs a good run but not your dad's Stage 1.
So I went right for the limit -
The last dyno run Tom plans is a fairly mild 250, with a low boost Turbo. I put this very streetable engine in your car and the Gonkulator said:
14.23 at 96.9mph
You and your dad will be right even to 60mph, but you should finish about a carlength ahead. A race that close is a real rush, my wife has had one or two of those herself and loves it.

I didn't think that mild turbo would take on the Stage 1, but if Tom Lowe's dyno results turn out like the Gonkulator says, it is possible. Stay tuned.

Nice car BTW! \:\)