On the subject:
Firestone/Bridgestone made some repro bike tires at one point a few years ago they were big for customs in Japan, they were not car tires.
The Coker tires Home | Coker Tire in those sizes are car tires (the Dark Side) and have an edge to them that is unsuitable IMHO for cornering.
Probably OK for cruising to the coffee shoppe on the straight road.
There are rib bike tires available from various manufacturers, but I'm not sure of the sizes and they won't say "Firestone"
But you are free to choose bad ideas off the internet.
Here's a good video on the plusses and minuses of car tires:
400-19 is a cycle tire thus the stock VT600 rim probably won't be wide enough. The car tire should fit the rear w/o any issue. The cost is definitely up there and past Avon Diamonds thats for sure. I suggest using a set of Shinko's instead with stock setup until you decide the "bob" look is going to work out. They're affordable and very sticky.
The Honda VLX (VT600) had:
19 x 2.15 rim on the front, which should accommodate a tire from 90 to 120mm metric. A 4.00 x 19 is roughly equivalent to a 100/100 x 19 ( if that existed) It should fit without difficulty on the rim, but I'd anticipate a problem with tire clearance under the mudguard, since you are trying to go 10mm (~.40") taller. Stock tire is 100/90-19 on front.
15 x 3.5 rim on the rear, which is recommended for a tire from 140 to 150 metric. A 5.60 x 19 is roughly equivalent to a 142/100 x 19 ( if that existed), but since it's a car tire, it's intended for a 4.5" wide rim. Still, I think you'd be able to get it on the rim, since folks do manage to get moto tires up to 180 and larger on the stock 3.5 rims. Rear tire clearance is more complicated, since the mudguard is suspended above the tire on body. I'd expect there to be sufficient clearance, since the stock tire is 80% of 170 tall, which is 136mm. You're only looking for another 1/4". Stock tire is 170/80-15 on the rear. That's like a tire 6.7" wide x 5.4" tall.