Had Ihtilam during a long road trip while fasting

As the title says, I was recently on a 10+ hour road trip during which I slept for around a few hours. During this sleep, I unfortunately had Ihtilam/wet dream, now I know that Ihtilam in general doesn't break one's fast as long as he performs Ghusl and prays his prayers, but in my case, this occured while on the road, where it's impossible to find any place to perform Ghusl. So in my case, I was completely screwed on what to do (as I had to miss my my prayers due to being in a state of impurity).

Now that I have reached my destination and am able to perform Ghusl, my plan was to pray the Qaza of all the missed prayers and repent/make dua and also keeping an additional fast after Ramadan to potentially make up for this missed fast (in case it's invalid). I am just making this post to get a second opinion/guidance as my case is something whose answer can't be found online easily.