First let me apologize for the length of this post, it comes with a little back history.

My host provider, NewtworkSolutions, installs a base b2evolution version of 4.1.5 and then wants people to upgrade to the current versions.

Historically this has not been an issue for me. I have been able to take the 4.1.5 version and upgrade to 5.5.2 with out a hitch.

Currently, when I tried to install and upgrade the new installation, I consistently get the error message:

An unexpected error has occurred!
My SQL error!
Unknown storage engine 'MyISAM'(Errno-1286)
Your query:
CREATE TABLE sessions (
sess_ID .........

(see image below)

I initially attempted a manual upgrade from 4.1.5 to 6.6.7 and received this error.
I then restored everything and tried an upgrade from 4.1.5 to 5.5.2 which has historically worked, same error.
I then deleted the install and performed a clean install of 4.1.5, all seems to work fine.
I then attempted a manual upgrade from 4.1.5 to 4.1.6 and received the same error.
I then attempted a manual install with the option to delete and reset the MySQL database, same issue.

I've been researching the issue in the blogs and see that there may be an issue with versions of MySQL tightening up options.
When I checked into the MySQL version(s) that are running on the hosted site I found out that the new install of 4.1.5 was installed with a MySQL version of 5.6.0 where my other versions of b2evolution are installed on the MySQL version 5.0
In my research, I found some comments about how some of the optional issues in pre MySQL 5.5 have become mandated in the MySQL 5.5 and later.

Is this a possible reason for the error message? Is there, are there place(s) where I need to change a setting or two when trying to upgrade from 4.1.5 utilizing the MySQL version 5.6.0?

NetworkSolutions is also requesting to upgrade the MySQL version of the other b2evolution installation from 5.0 to 5.6.0 I am hesitant to do this with the current running blogs for concerns of the probability of issues. Do I have valid concerns or do you feel that upgrading a b2evolution (ver 5.5.2) should handle the MySQL upgrade okay?

If I had control over which MySQL version that I could be on, I would want to keep them all the same and set the 4.1.5 install to happen on a MySQL 5.0 version to see if the issue still exists, but that's not one of my options.