Hi and welcome 
I don't think you're barking up the wrong tree. You've mentionned several things that would be looked upon very positively, not least that you could give up work for a child, which isn't something everyone is able to do, and would be looked upon favourably IME. Advanced reading up on attachment and other adoption related issues, is also good - you'd be surprised how many people don't do that. You've not said anything which would make me think you wouldn't be able to find an agency to take you on, so it's ultimately about whether you come to a definite conclusion that adoption is for you (or not).
I do think you may have to accept a slightly larger age gap than you have been thinking about, because of how things are at the moment with many people looking for younger children. You are right that you would unlikely to be taken on by an agency before your youngest BC is about 3 or 4. There are a couple of people on here whose BC were about 2 when they were taken on, in my experience this is quite uncommon, but it does depend on where you live. From there, the target time to be approved is 6 months (it varies in practice) and the wait for a match is a case of how long is a piece of string, and your own preferences will factor in.
FWIW, there is a very large gap between my oldest and youngest, much bigger than you would have (19 years), and yet they are very close to each other and always have been. DS is closer to her than he is to his birth sister (my other daugher, with a significantly smaller age gap) and that's all about their personalities. So in my experience having an age gap of 4 or 5 years versus 2 or 3 is not likely to be a determining factor in how close they are. Some people find that an extra year or two can be very positive - reducing competition between siblings somewhat etc. If your BC had both started primary school by the time an AC moved in, you would have their school hours to really focus on your new child, which I think is a positive thing especially in the first year or couple of years. I do appreciate it's not what you would have liked in an ideal world, but I'm hoping I can provide some reassurance or something similar that it can be positive to let go of an ideal and embrace something slightly different - I always wanted about 4 children who were relatively close in age. It's obviously not worked out that way for me, but that hasn't been a bad thing.
With your age range, they will want an age gap between your children and a new child, but you need to choose your preferred age range based on what you feel comfortable with, and plan accordingly. If you don't actually want to go through the baby stage again, then waiting would be a good idea, but actually there's nothing wrong with wanting to adopt a child aged 0-2 (would be about ~8/9 months-2 years in practice), and yes you may have to wait longer, but again it's about what you can offer a child and which child would benefit from your household the most, and if that's a younger child, so be it. In my experience, yes, social services will generally prefer your BC to be slightly older - they would probably be thinking along the lines of your BC being in school and you thus having more hours in the day to devote to meeting your new childs needs.
In terms of ethnicity/religion/culture, it all depends on which ethnic background you or your DH are from, AND which county/area you live in now. There are many children from certain ethnic backgrounds waiting, but very few children from other ethnic backgrounds. There are fewer children with ethnic minority backgrounds living in rural areas, and many many in London, Birmingham etc. Does anywhere in Eastern Europe/the Caribbean/Pakistan feature in your family background (that's not an extensive list by any means). Many places are desperate for Muslim adoptive parents, there's a massive shortage. If your family make up is half Japanese on the other hand, there are very few children who are going to be an ethnic match. If you live in an LA where 95% of waiting children are all white British, it will also be more difficult for you - in that case you may want to consider going with a voluntary agency who can look to other counties immediately, or with an agency involved in a consortium, or who will let you look nationwide very quickly or who are comfortable with you adopting a child who is not an ethnic match. Basically, research your agency/area carefully, don't be afraid to ask them questions.