It’s worth noting that Rav Yehuda Fetaya zatza”l, the famous mekubal from Bavel who passed away in 1940s in Eretz Yisrael, writes (in his Sefer Minchat Yehuda) that the years of Moshiach don’t count in the cheshbon.
There will be 6000 years that the world will exist normally; the seventh year will be a shabbos, where the world will be spiritual (see there where he describes the process in depth); and in between will be the period of Moshiach, which could taken an indefinite period of time.
He compares it to Aliyos of Shabbos.
As he writes it, we can have 6 aliyos, then a whole bunch of “acharon” additional aliyos stuck in there, and then the “seventh” aliyah.
The fact that additional aliyos were inserted doesn’t change the makeup of the 7 aliyos.
He says it will be the same regarding moshiach; the years of moshiach don’t fit in to the normal 7000 year plan we are used to hearing about.