Database design, many rows or many columns?
MySQL has limits, such as 1017 columns in an InnoDB table (as of 5.6.9).

If you are not filtering or sorting on most of the columns, put them in a JSON string and put that string in a TEXT (or maybe MEDIUMTEXT) column.

A key-value store can lead to lots of JOINs.  The limit is 61.

I'm confused -- Do you have 1000 sets of 7000 parameters?  Or what?  If it is a single set of parameters, then a single key-value table makes some sense.