I would leave the screws alone unless you have both a dedicated set of gun screwdrivers and some experience in this area. You may very well bugger them finding out they are too tight.
Join the PGCA, get that letter and find a good gunsmith who works with doubles to check this nice Parker out before you think of shooting it. The minimum barrel thickness and the entire interior of the barrels should be checked. If you do decide to fire it, use light loads, like those made by RST, with the correct length for your shorter chmbers.

Ben: Did your Grandfather have any other grandchildren that would be interested in this gun so you could keep it in the family. If he did the thing to do would be to give it to them. Thomas

The dogs head buttplate is a curiosity since a DH grade gun would be standard with an SSBP unless ordered otherwise specially. Other grade 3 or higher guns have been observed on occation with a DHPB, so it is not an impossibility. One thing I notice about your gun is that the buttplate screw heads are not engraved. Grade 1 and 2 guns of this era would have engraved buttplate screws. So my thought are that if the DHBP was installed factory instead of an. SSBP, then the screws would be engraved.
A PGCA letter on this gun would be a great thing to get. If records exist, that could provide information about the buttplate.

Have no living relatives that are not "afraid" of guns.
Am no longer shooting so it's now just sitting in friend's gun safe.
Changed butt plate screws around and they now line up vertically.
Did not attempt to change the others (as Patrick pointed out - afraid of damaging the heads).

Any ideas on value?

I saw Steven Cobb buy one like that from Asa Kelley for $2500, he being a dealer probably sold again for $ 3000

Thanks Pat.
Just needed an approximate value.

I think that may be a little high, I would be around the $2000 to $2500 from what I saw at Housemans Shoot and the WI shoot the last couple of weekends

And a major determining factor in value is confirming if that buttplate is original. Either with a letter or physical evidence. The underside of it can be a clue. The look of the wood under the plate might hint to it being factory or not. Also, sometimes the last couple numbers of the serial number were written in chalk or wax pencil on both the wood and plate on factory installations.

If the dhbp can be confirmed as original, and being a half pistol grip gun with good bores (by the looks of it) it MAY be worth as much as $3k to the right buyer. But I would not say any more than that.

Ben,

If you find someone with the correct screwdriver bits, for that year the floor plate screws will be two short ones and a long one. One of the short screws will have a slot across the threaded end. This is for the left side, under the left barrel. The long one goes in the back at the trigger guard. That is if nothing has been replaced.

Thanks again for all the help.
Didn't see any chalk or wax markings under buttplate when I reversed the screws.