Dear K.,
I'm taking a different perspective with my answer. You don't mention his teachers expressing behavior concerns. What that means to me is that his dependency may not be quite as ingrained or serious as you think. I still think you should have evaluations done, though. If you can arrange now for him to get AG (academically gifted) support in kindergarten, you'll be ahead of the game.
My kids were spaced the same as yours and I worked full time while my husband was in school. I had my own need for my oldest to keep herself occupied while I was busy with the other kids and with juggling life. I lucked out because she was capable of playing in the corner or playing with the younger boys to keep herself occupied. If my middle son had been the oldest, I would have had problems similar to yours. He is extremely bright and has always felt more threatened by my attention to the others.
I think your son is probably being more needy right now because of the presence of the 2 month old. "Negative attention is better than no attention at all."
An analogy to younger siblings:
The husband brings home a new lover and says to his wife, "Hi Honey! I've brought home another wife just like you. Don't worry, I have enough love in me for both (all) of you ... and when she get a little older, you can play together. For now, though, she needs more of my time and energy, so I'm going to hold her and play with her all the time. Just go and play nicely alone in the corner and don't bother us while I keep her entertained and meet all of her needs. Just be nice and gentle with her while she's getting used to our world. And when she's older, she can have your old (valuable jewelry), crib/bed/high chair/stroller/room/bike/toys, etc... but don't break anything of hers!"
Give him a solid 15-30 minutes "alone time" every day. Have him help you to schedule the time. "When the other two are sound asleep with their naps, we can have our alone time." Read, have him help you make dinner, mate socks, fold washcloths, bake cookies, build Legos, ... Let him know how valuable it is having someone as grownup as him helping you when you have so much to do.
Try bringing home a couple of the small Lego kits. Let your son know that these are just for him, just for bigger kids because the pieces are too small to be safe for the other boys. Show him and work with him on how to follow the directions building the first one, then put it up on the mantle or someplace prominent and safe. Give him a second one. Encourage him to build this one himself. If he doesn't, work with him a bit until that one is built. Same with the third. Give him a sticker on a chart for each one, even if you've helped. Eventually, he has to do them himself, of course. Feel it out. When he has built 5 and has 5 stickers, then he has earned the ability to go with you and pick out the next one that he will do himself. When that one is done, etc. ...
Some call it bribery, but I became a great believer in using stickers/stars and sticker charts to maneuver the behavior of my children because the system worked!!
Just so you know, my middle son's testing when he was 4 y/o didn't reveal his ADHD. The psychologist checked his IQ, nothing else at the time, and said he would be reading in 2 weeks. I didn't realize that he needed a more complete psychological assessment until he was 7. He was the youngest identified AG student in the school, and the only kid in his first grade class who couldn't even read a sentence. This was three years later!
Good luck!!