Hi climba,
We have a birth child but have decided to (try to) adopt our second child, rather than try to conceive again. Accordingly, we had similar concerns: We were clear that if we for some reason or other couldn't adopt, we would want to try for another birth child; so time was not on our side.
We initially wanted to wait until our DS was 8 or so, to start the process; but that would have put me solidly past 40, and if we were then told 'no we won't assess you because of x' we would have been devastated, probably having missed the boat for having any more children by any 'method'. (Also, assume we did then manage to conceive again, the age gap between our children would be 8 or 9 years at least, which is again not something we really wanted). So when the time came where we were totally certain that we wanted more children, and did not want to risk never being able to have more children, we started making inquiries. From some perspectives it wasn't the ideal time to get started, but putting it off any longer started to feel way too risky.
Regarding the issues you worry about, we had a few of those too. One of ours was that we speak a different language at home, and we were worried that this alone would rule us out. What we did (nearly a year ago now): We called First4Adoption, and got to talk to a great, knowledgeable, wise person who was able to reassure us that provided we had a 'plan', this should not stop us from adopting. She also told us that we should call agencies and not be disheartened if some 'declined' us, there would always be another one who would be keen to take us on. So we did. And here we are, panel coming up soon - we still can't know for sure that we will be approved to adopt, but chances are pretty good, and indeed if everything should go wrong, we are still young enough to consider trying to conceive again.
I'll be honest though: Starting the process when we did, did come at a cost. It's complicated to explain fully, but I will never now have the kind of career I might have otherwise had (i.e. if we had waited and started the process later). However at some point I had the personal insight that I would rather risk that career, than risk never having any more children.
I think it boils down to how old you are, how worried you are about your fertility, and how much you want to have children. If having children is a top priority in your life, and time is running out with regards to fertility, then you should definitely make inquiries. Find out if an agency would take you on. Lay your cards on the table, discuss the issues that worry you, and see what they say. They might reassure you that you sound like ideal adopters and if you WERE reassured, you could delay starting the process for another year or two. Or you may decide that actually, you want to get things going NOW.
A couple in our prep group started the process days after their second BC was born (our LA is quite unorthodox in some ways!). When their youngest turned two, they finished it, and were then ready to adopt a baby. What I'm saying here is, there are also options of building delays into the process. So if you start now, do stage 1, then wait (up to six months) then do stage 2, then you may have a wait for a good match, then you wouldn't be that far off those 2 years when finances will get easier for you.