I know nothing of Fusion but do use Freecad and I like it a lot-in spite of it's quirks.It takes a slightly different approach to get to grips with parametric modelling and you get a lot more versatility once you make the leap.The Draft workbench might be the best place to start drawing things but for machining I stay with the Part Design workbench as the solid models you can easily create make it easy to create the toolpaths and you can run a simulation to see the part appear in the manner that the machine will cut it.I recommend an hour or two watching the videos on youtube-sliptonic and Joko engineering are very good.

I'd have reservations about either laser cutting or waterjets because of the edge conditions they leave and it also wouldn't be possible to cut the scarphs.The scorched edge of a laser cut might not be the ideal surface for bonding and the pressure of a waterjet-they can operate at 60,000 psi-might drive water into the plywood and need a good deal of drying.If using either it would be worth doing some experiments to verify that the bonds would be sound.

Once you have the level of proficiency with a chosen CAD system you might like to try nesting the parts so that you can try presenting a cutting business with a project that has a good deal of the legwork done.They will thank you for making sure the outline entities are joined together and then they can just select the tools and the cutting depths and I would expect their software to give a good idea of the time needed and hence the cost you would bear.I would expect a quick google for CNC router services in Hampshire or Dorset would turn up a few.

It has to be said that conventional flat bed machines will outnumber tilted machines by a huge factor.If you are looking to acquire one you will need a healthy amount of electricity to run it because it will need extraction and quite possibly a vacuum pump.All of which will eat up workshop space