We have these roughly 3-inch by 1-inch slotted drains that run along our pool deck. I recently had a guy come and pressure wash the rear of our house and the pool deck, and he blew those drains out, and in the process discovered I have some serious issues with getting the water/debris to move. Additionally, we have had problems with water pooling up and dirt washing up onto the corner of the patio pictured below.

This is the corner where we have the most issues with water pooling and with debris (mostly dirt/mud) backing up onto and across the pool deck. That drain was completely impacted with mud, and I had to dig a trench (which you can see in the other attached photo) so the pressure washer could finish his work without water just standing on the pool deck.
I am currently thinking I can route the water away from the drain end and into a small catch basin with a top grate to handle excess water coming from the lawn, then ultimate direct the water from the catch basin down a pipe, maybe 5 feet away to a larger dry well style installation. See the other attached image for a wider look at things.
Two questions: 1) what can I use to hook into the end of that drain and direct the water off toward the catch basin, and 2) does this plan sound reasonable or am I missing a better/easier solution?
Thanks!

This is the corner where we have the most issues with water pooling and with debris (mostly dirt/mud) backing up onto and across the pool deck. That drain was completely impacted with mud, and I had to dig a trench (which you can see in the other attached photo) so the pressure washer could finish his work without water just standing on the pool deck.
I am currently thinking I can route the water away from the drain end and into a small catch basin with a top grate to handle excess water coming from the lawn, then ultimate direct the water from the catch basin down a pipe, maybe 5 feet away to a larger dry well style installation. See the other attached image for a wider look at things.
Two questions: 1) what can I use to hook into the end of that drain and direct the water off toward the catch basin, and 2) does this plan sound reasonable or am I missing a better/easier solution?
Thanks!