Yeah can imagine it might take a while. I'm great when it comes to meeting people but I find the online aspect of chatting a lot more difficult. I think it's because it's not a fluid chat, there's gaps and waiting for the replies and all sorts. When it comes to meeting someone in person I have no issues. I'm a confident, upbeat kind of guy but that's hard to show by merely messaging. It's difficult getting a know a girl or find a match, let alone getting an actual date! Just hoping my luck changes.
That is why you 1) move away from the site/app and 2) set up a date as soon as possible. You mentioned that you were messaging for a week before asking the last girl out. In general, that is too long. You should be getting their number (don't bother with Facebook, Instagram, etc) and setting up a date within a few days, if that long.
A lot of people on OLD sites are content with having people as texting buddies (for the self esteem boost, their social anxiety, them being in a relationship, lying on their profile, etc) and will never actually go out with anyone. It's best to weed out those sorts of people as soon as possible. If they say "it's too soon" or "I need to get to know you more", move on. The actual date should be where you are getting to know someone, not by messaging someone for weeks or months before they deem you worthy to actually see them in person.
Also be specific and firm when asking someone out - "let's meet a XYZ at Saturday at 7 for a drink". Don't go back and forth deciding when/what to do - "do you maybe want to do something sometime?". It makes you look wishy/washy.