Hmmmm upgrade advice

Evans do good demos - you have to book and pay a deposit, but they can get almost anything in for you. Talk to them about how long you can have it for, I had a couple of bikes for an hour each, helped me to choose

I'd also vote for the drops, if only for the hand positions (the wind cheating is nice even if you're not going too fast as an often needed physchological tool against headwinds). If you're reaching over the £1,000 mark then hydro discs are a must-have for me, particularly if fitness is your aim -better stopping in the winter and particularly on longish descents in the cold is well worth the extra couple hundred grams IMHO. The Search and Arkrose are good picks ... I'd add in the Raleigh Mustang and the GT Grade as bikes to look at.

But do try to get a loaner road bike for a while, the handling with drops is different, and if drops aren't your thing well then there's no one paying to use them Flat bars are much better off road, and hilly terrain does considerably negate some of the advantages of drops.

I used to ride a MTB, then realised I was spending more and more time on the road so I kitted it out with slick tyres and bar ends.  That worked for a couple of years but I couldn't ride it far enough or fast enough; the wide bars and upright position were a major hindrance.  So at the ripe old age of 50 I treated myself to a proper drop barred road bike.  So much better in every respect.  That was 8 years ago and now it has a lighter, carbon framed stablemate.  The only other thing I'd recommend is if you plan on riding in the wet, get a bike that takes proper mudguards (my first one does)

Another vote for drop handlebars.  Apart from anything else, you have something like 4 or 5 different places to put your hands, which then also affects the rest of your upper body.  For half an hour rides, it won't matter, but as you get into longer rides it makes a huge difference.  It also saves you energy when the wind picks up, or when you are tanking downhill.  At first it may feel skittish, but you will get used to it.  Cynically, I think flat bar bikes/hybrids are the bike industry niche marketing because a lot of people get a hybrid and then when they get the bug realise it's a jack of all trades...

I got bar-ends for my mountain bike as just having one place to put your hands on the otherwise flat bars really got on my nerves.

Otherwise the adventure road bike seems a good fit for the riding you describe.  I disagree about disc brakes though, yes they are way better than rim brakes in the rain, but you will lose out elsewhere in the spec of  your bike if you go with discs now.  Maybe in 5 years time prices will come down etc.

Using drops makes a bike very versatile in position. So relieving discomfort and cramps by adjusting hand positions

get someone to lend you a proper road bike in your size for a week or so.  Really. You must.  Or else you will be risking  spunking your money away.  The owner of my LBS lent me one of his bikes for 10 days.  There are these guys out there.

My personal experience-  started riding 100ish miles a week on an old heavy Marin city hybrid and decided to treat myself to a new bike.  Chose a very nice light frame but asked LBS to build it up with flat bars.  They basically bullied me into riding one of their own bikes with drop bars before they would do my build with flat bars.  My build had drop bars.  No question.

My wife's experience- started riding more regularly so wanted to upgrade her old heavy Marin city hybrid.  Based on my experience, we bought a drop bar road bike.  She found it a bit skittish, so also bought a very nice, very light, flat bar bike.  Which now mostly stays in the shed, because with a few more miles under her belt she is back on the drop bar, which no longer feels skittish, it just feels right.

What I would say is, increase your budget to get hydraulic disc brakes.  Just in a different league to anything else in terms of stopping power until you get to stupidly expensive rim brakes.  (The only rim brakes I have used that are even close to pretty basic hydro discs are Campag Super Record)

It's spooky how similar your description is to me,  dusted down an old hybrid bike I've had for years last summer and now have the bug.  I also ride for fitness with similar rides as you describe. 

This summer I bought a Btwin Triban 540 flat bar, and can't recommend it enough. Fantastic spec for 500 quid and a joy to ride. It's fast and light,  it very much is a road bike with a flat bar. It can take tyres up to 32mm, so can change tyres if rougher roads or trails part of regular ride. That said I thought first thing I would do would be buy 28mm tyres,  but the 25mm stock tyres were not as intimidating as I thought. 

I did my first sportive in September,  a 45 miler, and the bike coped well and was on a par with most riders on drop bars.

However, having had go on a drop bar recently, I have now started thinking I should have gone down that route,  getting down onto the drops into the wind made life so much easier.  I can get aero on the flat bars but it's uncomfortable and not a position I can hold for too long