I wonder if you could fit the Sonex's engine in a BD5J? That might revitalize the design. For what is worth, the BD looks a thousand times more refined than the Sonex. Of course, the thin tapered wing probably leads to some nasty tip stall behavior on the BD.

there are many other issues just as big as the engine

The sonex model line are well-engineered kits with detailed instructions, factory build support, and the parts are all high-quality and fit together with no fuss.

There is a reason almost no BD5 kits (piston or jet) were ever completely assembled. There is a giant chasm between designing a neat airplane, and designing one that can actually be built by regular people using attainable skills and tools.

We had a captain at SWA in the old days that killed himself in one.

there are many other issues just as big as the engine

The sonex model line are well-engineered kits with detailed instructions, factory build support, and the parts are all high-quality and fit together with no fuss.

There is a reason almost no BD5 kits (piston or jet) were ever completely assembled. There is a giant chasm between designing a neat airplane, and designing one that can actually be built by regular people using attainable skills and tools.

According to wikipedia, around 5000 kits were sold and a few hundred were completed. I think that a large part of the problem was that it was marketed at a low price point and was supposed to be buildable without special skills. Cheap and easy attracts a lot of builders who can't fix any problems in the kit.

What I've learned about the BD-5:

Those that have flown a properly-built BD-5, within it's small CG range, say it is a wonderful experience.
Light, well-balanced controls, easy to fly.

But...

If the kit was built strictly by the instructions, it was crooked and unsafe.
Many of the assembly instructions have the builder measure from the edges of a panel, but the subcontractor responsible for the hydroformed parts with compound curves did not cut to final dimensions. They assumed the builder would trim, but there are no dimensions given in the plans.
After the first few customer built airplanes earned a horrific safety record, it was determined that a BD-5 must be built in a jig.

Also- The BD-5 was designed for a lightweight, 2-cycle air-cooled engine.
Several engines have been used, many heavier 4-cycle liquid cooled that throw the CG out of whack, needing lead weight added to the nose.
Instead of stalling around 60 knots, it now stalls around 80, requiring longer runways, and much higher impact speeds in case of an emergency landing.

Build it straight in a jig, keep engine weight to a minimum, and it should be a fun toy.

Small size makes it worse, tighter tolerances requiring a level of precision difficult to achieve with just a regular home shop.

I too was dreaming of building one of these.

But I ended up with a Tripacer.