Well it makes sense, now, why he's not eating as much hay. The pellets should be timothy-based. Alfalfa pellets are too rich for rabbits over 6 months of age. He's old enough for adult rabbit pellets. Oxbow has adult versions which should be timothy-based.
Also, carrots are super high in sugar -- another thing that can cause a rabbit to favor the sweets over the hay. He doesn't need any carrot at all if he's not eating enough hay. The green tops of the carrots are great for him. The carrot itself should be limited to no more than a 1" slice per day. But I think I would stick to just the green tops for now until he gets his diet sorted.
Your idea to add a variety of greens (think more in terms of 'greens' than 'veggies,') is good too. But maybe it would be best to not change too much of his diet all at once.
I'd suggest first transitioning him to the right pellets. It's good to do this by mixing the old pellets with the new over several days so as not to upset his tummy.
This explains more how to transition. I'd also cut back on that carrot during this time.
Once he's gotten used to the new pellets, then you can cut out the carrot altogether (except for the green tops), and slowly begin introducing new greens. This should be done one new type at a time.
This section explains how to introduce greens safely.
Once he's eating the healthier, timothy-based pellets and a variety of greens (and less sweet carrot) he should start munching on hay more. Refreshing the hay a couple times per day also encourages more hay eating.
If he's an average (5-7 lb) rabbit, once he's on the good pellets and a variety of daily greens, the pellet amount should be just 1/4 cup per day.
