Does anybody think that current climate models handle this correctly?

Landscheidt Cycles Research » Latest Solar Differential Rotation Information.

In the next graphic we go back further and it displays exactly what I have been looking for. During past grand minima, observations suggest a faster rotating Sun, as can be seen at the equator. After 2000 there is a greater acceleration occurring.

Also noted is the much longer length of cycle 23 (96- ?) compared to cycle 22 (86-96). So here we see two direct links to the highly possible effect from Angular Momentum created by the Gas Giants, increased rotation rate and the stretching of the cycle length as the Sun takes its abnormal path every 172 years.

The last time this occurred was in SC4 just before the Dalton Minimum and the retrograde motion we are now part of is very similar to SC4. On average the retrograde orbit (purple) is around 9 years, SC23 & SC4 have orbits of over 11 years.