To follow the minuteman questline, you have to end up with 8 settlements. Unfortunately, you have to take whatever random settlements Preston gives you, instead of the ones you would like to take in the order you would like to take them.

You can take settlements on your own, but they don't count. Preston isn't giving you the take the castle quest until you have 4 proper minutemen settlements, and isn't giving you defend the castle until you have 8, and they have to be the ones that he gave you quests to get.

Is there a way around this?

I'm not sure if this is the best place to ask this question. In the speedrun we only deal with one settlement (and by deal with I do mean kill), we're able to still complete the game after because of many skips and sequence breaks. If you're just trying to complete the game casually, I would ask a different forum, because using our methods will probably seem really cheaty in a casual playthrough.

It actually does relate to a speedrun, but a glitchless speedrun.

The few people who have done a glitchless speedrun of fallout 4 have done it via the institute quest line. I'm trying to figure out whether it could be done quicker via the minutemen quest line. But it would only work if the settlements could be easily acquired, which would mean getting them on your own. Getting them through preston garvey takes forever.