I wonder if it could be your "clock ticking."
I was never pregnant, wanted babies but was single when single motherhood was undesirable, and had a strong desire to have a baby until I was in my 40's. So I adopted an older special needs child which may have been what cured my "ticking clock."
I suggest that your emotions, whatever is causing them, need to be counter balanced with reality. Your description of your family sounds to me like having another baby would present numerous difficulties for you and your family.
I have a granddaughter who exhibits some ADD markers and a grandson with speech apraxia. Developmental delays get more complicated as a child gets closer to school age. In 2-4 years your oldest daughter will be entering her teen years which are universally known to be difficult. She especially needs as much positive attention from you as possible now continuing on thru the teen years. With a developmentally delayed 3 yo and a colicky baby for the first 5 1/2 months taking most of your time where does your 10 year old fit in now?
As you said you have your hands full!
I've experienced the strong desire to marry someone I loved and found that I was greatful that I had listened to my brain instead of my heart. He is an alcoholic and has now been divorced twice. We have to listen to reason as well as follow our heart. The two need to be balanced.
I'm wondering if it's possible part of your want/need is related to wanting a baby who is warm, cuddly, and in many ways much easier to care for than a preteen and a develpmentally delayed daughter. Your baby has not and sounds like he's still not the easiest to take care of. Maybe this baby you're wanting will be the perfect baby.
Anyway, since you're thinking 2-4 years down the road this is most likely not a decision you have to make now. Unless you're considering a tubal ligation or a vasectomy.
You are fortunate to be able to stay home with your children. I wonder if getting recreationally involved outside the home might help to allay your want/need. Perhaps the wish for another baby is your wish to be involved with life disguised as a wish for a baby. Being with your kids all of the time is not easy. If you don't have an outside interest/hobby/close friends, life can become tiring and dull. "Same ole, same ole." Another baby would enliven things up for awhile.
As an aside, are you getting professional help with your almost 3 year old? If not your school district will provide an assessment and professional help without charge. It's mandated by Federal law. The law also provides more money for children under the age of 3. We didn't get my grandson involved until a couple of months before his third birthday and he missed out on much needed therapy.
I do empathize with your feelings for another baby. I've had those feelings. I handled them by not focusing on them. They were still there but I knew that I had a "real" life to live. Looking back, I realize that I unconsciously stopped using birth control. I knew I didn't want the difficulties of being pregnant as a single mother but I really did want a baby. This was happening in the 70's when unwed mothers weren't very well accepted. When I adopted in the late 80's my supervisor told me it wasn't right for me to do so because I was unmarried. I'm glad that times have changed.