Well I'm the new owner of a 2019 Roadster 110 Anniversary Edition with all the bells and whilstles (power steering, 5 link adjustable rear suspension, adjustable front suspension, uprated brakes) which I have purchased specifically for extended touring. You will maybe just about get a 3.7 ltr Roadster at the top end of your budget or a higher spec 3ltr one otherwise.
For now (and maybe for good... don't tell the missus!), I still have the 1999 4/4 which I got in 2017 for fun on the B-roads, which it excels at with skinny tyres and no power steering. Bloody great fun, but a bit more of an effort on longer journey's and faster roads. I woudn't really try and compare the 4/4 vs the Roadster - the experiences are so far apart.
My original intention upgrade wise was a +4 Works Edition with the re-mapped ECU and uprated exhaust system - I lost out on Steve Morris' (former Morgan CEO) low mileage one at Silverstone auction - which I think would have been fine for touring, but the Roadster popped up at a non-Morgan dealership at a decent price so I snapped that up! What's not to like about more power? Oh, that's right... higher insurance costs and naffer fuel consumption, but I don't really worry about those things!

Dave W is the best person to give you the comparitive merits of the uprated +4 versus the Roadster.
As important is your travelling luggage. I have a choice of fitted Classic Travelling Luggage fitted cases (formerly Hills Alive) behind the seats vs some Morgan branded Connelly Leather branded overnight bags which slot in, and a leather suitcase (identical to the branded ones, bar the embossed logo) versus a 120ltr waterproof holdall. I use the fitted cases and the holdall for longer trips and the nice leather stuff for long weekends (...or if I want to kid people on I'm posh!).
As others have said... test drives, or even weekend hire, will give you a personal flavour of the choices.