My son was 9 1/2 pounds at birth (41 weeks), so 96 centile. He's the biggest baby in my family and my partner's family... no idea where this huge baby came from, but he came out C-section because his head was too big, etc.
I digress. He was holding his head up very early too, his neck is very strong (partner's family trait). At 4 months, he was breastfeeding pretty much constantly, as you described. I was exclusively breastfeeding and we were spending all our time nursing, and I was desperate for some sleep. People said he might be ready for a rusk, and I hesitated because of the new guidelines to not give them food before 6 months. But I was desperate, and he was clearly very hungry.
I bought a box of rusks, and when I let him try one he nearly bit my hand off. That convinced me. I bought these round ones, and cut them into thirds, making little sticks he could grasp. He would get one after his naps, or after a feed. He really looked forward to those. After a few weeks of this, I would dissolve a bit of rusk in some breastmilk and make a very thin porridge, to get him used to a spoon. We started him on baby rice the day he turned 5 months old... I know there's no calories in it, but he was still sucking down the breastmilk and need a little solids in him just to make him feel fuller.
This is not what I planned. I wanted to go by the guidelines, etc, but I had a huge baby, and you have to be flexible. He's nearly 1 and still breastfeeding, but not like before, because boy has he discovered food. He loves it all, especially Sunday roast dinner. I suggest you start out gently with the rusks and making them into thin porridge and see how you go from there. Good luck!