I can understand your reasons for wanting to do another PhD but I'm not sure it's a good idea as it's unusual for people to do a second PhD! Most people have had enough after doing their first one and then want to move on with their lives. A PhD opens doors to other opportunities you may not have had or previously thought about! What about doing a RA post - there is less pressure there to publish and you would probably get flexible hours as long as you check with your supervisor as academia is very flexible!
However, in current situation there are definitely more PhDs going than anything else so you might as well give it a go! I've seen some really interesting PhDs that I think would make great postdocs but that's not to be especially as it's so much cheaper to get PhDs in to do the work! You need to be prepared for questions as to why you want to do another PhD? Can you get experience in Education by other means e.g. RA, work experience etc...?
It's great you are enjoying your PhD so much which makes a change from the stories here. :p