Terry;

An 8 by 8 Girder / Summer / Tie Beam, with 4 Inch Wide, 5 Inch Deep and 2 Inch Long Pockets?

Designed to carry 2 Inch Decking and a 6,000 Pound Rolling Load? That's a Pretty Intense Point Load, By The Way.

and, when you say;
Do you mean that only One Bay will have Joist Pockets or merely that your Joists do not line up?

(Grain would still be severed, however)

This seems like an extraordinary section loss, to me, personally the floor seems Very Spongy from what little information you've given, and I don't see how wedging the joint could make up for your piercing the Compression Band in such an extreme manner.

Joinery is a compromise, and is a large element in design (Sizing Timbers as an example). In This case,

Not knowing How many Joists, what centers, whether only One side (One Bay of Joists) or Multiple Bays of Joists merely "Stagered" ("CheckerBoard Style")

And designing to carry significant Loads I would probably go with deeper Beams, say an 8 by 10 minimum, and go with a soffit tenon with stepped housings, rather than a drop in pocket, in an effort to reduce as little of my Carrying stick as possible, placing my section loss as close to the neutral axis as possible, while still endevoring to house as much of the Joist as possible.

I couldn't tell you how I would design for a One and a Half Ton Vehicle, as, I have never had to design for this type of Load before, and simply don't have that knowledge at the top of my head.

But, if you are counting on Wedges to stiffen this 8 By 8, and to compensate for your Drop-Ins, I think you should reconsider.

I would also ask what made you look at this particular Joint, and this particular Dimension (8 x 8).

Tim Berube