Well done.
I found the same. I started in August with rasping lungs and raging thighs after 1.5 miles!
I struggled for weeks fighting the darned bike to go quicker, and failing miserably. Eventually, I did exactly as you, and thought, you know what, just enjoy it.
I'm now perfectly happy to cover 15 miles, and have felt so good at the end of that distance the last couple of times that this Sundays ride will be 20 miles.
Funny, but taking it easier nit only made it more enjoyable and less physically stressful, but it also made me move quicker with seemingly less effort. Like with most sports activity, relaxation goes a long way.
Keep it fun, smooth and without the flat-out battle every time, and you'll soon see your distance improving.