lumens confusion.

Hi.
Been lurking on site learning lots but am now confused. (easy for me!)
almost at end of first grow with new room and setup. 8x8 foot. 12 feet high. running 4 600 sodiums. vegging clones in other rooms under t5 and 250 sodium. soil grow. temp and humidity are within ranges i think. nutrients mainly biobizz or canna terra.
i want to up yields now and start tweaking the system.
i calculated 4000 lumens per sq foot....i think. plants are about a foot under lights.
should i think about moving up to bigger lights? heat etc would need watching. i did a yield calculator just out of interest....it said 64 oz????? surely not??? :0
plants are about 4 foot at finish although i am not sure if this isn't too big?
thanks for any advice tips on how to move forward from here. i am reading up on filming topping pruning techniques and maybe one day trying a scrog.
strains at present mainly www x bb and am vegging various skunk too.
Thanks 4 reading and any feedback.

5,000 lumens/sqft for flowering is pretty much a minimum.

Either bump up the lights, or make the room a bit smaller. Be easier and cheaper to decrease the size of the room.

Wet

Lumens
Usually a garden should have around 1000 to 3000 lumens of light for every square foot of space. Most gardens that are successful and grow decent marijuana plants will have about 2000 lumens in a square foot. When the dope plants reach the vegetative stage they will begin to stretch out more and the weed plants will not absorb as much light. When the flowering stage occurs the marijuana plants become a lot looser though.

Knowing the technical side of growing marijuana plants could be the key to success. It is not as simple as getting all of the equipment and putting it to work. You have to make sure that you have everything measured and calculated so your marijuana plants are taken care of in every aspect so they grow successfully. Marijuana plants definitely need to get enough light so make sure that they are getting at least around 2000 lumens of light per square foot so you know you won’t end up with dead marijuana plants.

Guys
thx so much for replies...2000 or 5000??? or am i really confused and misunderstanding? i read 7000 per sq foot?
i worked out 8ft x 8ft = 64 sq foot
600 watts x 4 = 2400
2400 watts x 107 lumens = 256000
256000 divided by 64 = 4000
approx figures rounded down
not really sure i have worked that out correctly?
I realise i have a lot more to learn and read up. i just thought lighting was an important place to make sure is right and follow on with environment nutrients mediums strains and develop my own technique as i gain experience?

plants are looking good i think...learned loads by trial and error. but want to get better.
thank you again advice!