International layover at IAH

Hey!

In a few weeks, my partner and I will be transiting through Houston IAH on our trip from an EU country to a South American country. On our leg back, we are arriving in Houston at 5.30 in the morning and departing at 16.30. This is in theory a fairly long layover which we thought to utilise with a trip to the city. We're not really fans of renting a car on another continent for a day, so we'd take public transport.

I'm a huge rocket nerd and was excited at the chance of getting to see Houston Space Centre, but google doesn't even show me options of getting there with public transit, the distance is a fair drive and I can't seem to find any affordable airport transfers. I think I'm a bit spoiled by the prevalence of fast and simple train connections in Europe, so the distance seems doable, but from tripadvisor posts it seems 10h just is not enough to reliably make it to the space centre and back through the airport (people were referring to 3h treks on public transport etc). Point is, seems like a fleeting dream – can anyone advise if it is a very bad/unrealistic idea, or if there is a way to do it reasonably?

Do you guys think it is even worth it to leave the airport? I'm curious to at least see downtown and get a meal, which seems more doable with the METRO buses. But if it's at the cost of missing a transatlantic flight, I'll pass.

In advance, thank you for the advice!

TL;DR: 11h layover at IAH. Is it worth leaving the airport? Is space centre houston viable to visit in that time (I'm guessing no)?