I dont know alot about crossing pinnate palms with Palmate palm trees.Alot of palms will cross naturally,Butias is one species that does this alot.I have 4 mule palms and I'm going to try to cross one of them back with a Butia Capitata.To get a more cold hardy coconut looking palm.

Someone on EPS has tried to pollinate ChamaeropsxFortunei and is awaiting results in the next month.
I theory Chamaerops,Needles and Trachys are close enough genetically to try crossing.

There is a crossing that I really like.It's two Trachycarpus palms.It's on the website of Three Rivers Palms.It's called a Trachycarpus Takaghii.It looks like a drawf T. Wagnerianus.It's a T.Fortunei x T. Wagnerianus.

I just got one of those last week,it's the one in the center in front of the bananas-one of my favorites also!

Mule palms are sterile, hence the name "Mule".

Those would be some really cool hybrids if someone could do them Neon, although I've personally never heard of anyone ever successfully pulling any of them. The Chamaerops x Fortunei cross sounds pretty exiting. I personally have some roebelenii x dactylifera and roebelenii x rupicola seedlings but those aren't as exotic as what you're asking.

There is someone on the westcoast that claims to have a butia x cocos hybrid. That's an exotic one.

BTW

Your Trithrinax looks great Jim! Mine keeps getting brown spots on it's new leaves, but I've recently moved it into the shade and have noticed that the new leaves are fine. Are you growing yours in the shade?

I dont plan to try to get the seeds from the mule palm.I'm going to get the seeds from the Butia Capitata.That's where mule palm seeds come from.

Andy the Mule palm seed in general is sterile. However you can take the pollen from it and pollinate other palms. Such as the Butia or the Syagrus. There are already many crosses out there like the Butia x syagrus x syagrus or Butia x syagrus x Butia. They are more commonly called Mule palm backcross. If you would like to see a photo of one I can send to you in a email.