I didn't see the examples you posted until I scrolled further.
First -- you illustrate perfectly that half the problem is speed. Most of the time people can improve legibility by slowing down.
Second -- you have several things going on that are already very nice that you can build on. The main one is your consistent slant.
Most of the time you have enough space between your letters. A common problem with legibility is that there is too little space between the letters.
Check your normal speed sample and notice the places where letters are touching. On the careful sample - all the letter spacing is perfect.
So, you are in a perfect position to start repairing things.
The two main areas to work on are:
taking the time to form letters that have enough space within the letters.
Keeping your x-height consistent.
When you write fast, certain letters are done so quickly, they become small and pinched -
At some point, you might want to analyze each letter - but for now, just look at the a, o, and e.
Some are quite a bit shorter than adjacent letters. Some are so tight there is no *counter* - the word used for the space enclosed by the letter.
And some are both.
There is no magical way to correct issues caused by speed. All you need to do is slow down. Eventually, your accuracy will improve and you can speed up naturally. Forcing yourself to write larger will help, but it will feel unnatural - so it's something to try. For some people it works very well, for others it is just annoying. You're the one who has to try everything and sort out what's right for you. Think of it a physical therapy for an injury. You don't have to do it forever, but it will speed the healing process if you can force yourself to do it for a little bit. Once you see some results, you might feel better about the process.
Side note on the Spencerian e -- it's very tricky to keep it open enough. On your careful sample, the a's and o's are all very nice. Some of the e's are pretty tight. Your careful sample shows that you have the basics down -- so your main task is to find a way to enjoy practicing and building up muscle memory and then rev up the speed gradually.