I did get a lapel mic, and that improved things a lot, but I figured I could do better.
As an example, with the previous mic https://youtu.be/mYBRTz2ReZQ
But with the new mic https://youtu.be/mjJaOKZ4S0c
The new lapel mic is itself a lot better it seems, a lot clearer. But also I got a shotgun mic. So when recording messing with cards I pointed the shotgun mic at the cards for sound effects, and it hardly picked up any dialogue at all, perfect. My first attempt at mixing in an effect track with a dialogue track. I'll get the hang of it yet.
The new lapel mic is Movo LV8-C and the new shotgun mic is RODE NTG2, but also needed an XLR lead and mic holder.
I also got a Tascam recorder, as it seems able to do 4 tracks of 96kHz/24 bit with no problem, which is nice. It actually seems like quite a nice recorder, but I seriously doubt it is a factor in sounding better.
Of course, this is also the kit I have here for when I do live TV broadcasts from here :-)