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I've been looking at this option lately as well. Just yesterday, I sent a print to BumbleJax to have face-mounted to 1/4" acrylic.
BumbleJax was my choice for some of what you mentioned vs. direct print to acrylic. Printing directly to acrylic will not give the same standard of resolution or vibrancy of a traditional print that is face-mounted to acrylic. The face-mounting process is sometimes called diasec, which you can google and find some information on. Here is a helpful thread on diasec:
I chose to print the image on my own and send it to BumbleJax to have mounted, but they will print for you as well and I believe they use an HP large-format. I printed onto LexJet Sunset Metallic with my Epson 9900 and signed the print before mailing it to them.