Just to add my average speed is 16mph on a 30 mile ride. Not 19mph. I wish

I get a slight burn in the thighs ... Is this the norm?
Don't worry about your speed. Work on endurance and the speed will come up by itself as you increase your base. As said, 800 isn't much. Your muscle tissue is still getting used to working in a cycling way. It's taken my body 4000 miles to really start to get the hang of it.
Get a heart rate monitor and do lots of tempo work, with a little threshold here and there. Go as slow as you need to to maintain this. It's AMAZING how fast this will work. Learn proper nutrition and hydration and the distances will rapidly extend.
The burn is normal.. Thats lactic acid building up. As you train that with threshold work the burn will happen later. Aim for achy muscles afterwards, the more ache the more muscle tissue rebuilding will take place, but only if you rest properly. If you fail to give yourself recovery time your body really will slow down any gains, as well as risking motivation losses.
As for slouching, yes core work will help. Don't go banzai in the gym tho, I would recommend Pilates instead.. Not the cattle market sports centre sessions though. Find a proper practitioner who will do both mat work and machines with no more than 5 in a class. You need someone that understands cyclists as well. I started said sessions 3 months ago and the difference is extraordinary.. I've even lowered the bars by about 4 inches and it feels amazing.
I've followed these steps and in a year I've gone from dying after 5 miles, to being able to ride for 100+ with ease. Every Saturday I do 70+ at an average of 18+mph.. We're all different though and I know I'm lucky enough to have a body that responds well to training.
Good luck.