This is based upon my personal experiences and opinions. Feel free to disagree
I wouldn't recommend fishing with rods over 7ft on the kayak. Imagine trying to secure/net the fish as its on the side of the kayak. If you have to reach quite far, you risk losing balance. You have to be able to secure the fish while staying balanced.
Why 7ft? This is the longest rod that I can take on my kayak that will fit into my fish/storage hatch. At the same time, I am a still able to comfortably net the fish and secure the rod in the holder. I imagine it would be somewhat more difficult if the rod is longer than 7ft. You could always use a longer net. Nothing wrong with that. I don't use them as they are not convenient for me to quickly pull out of my hatch and use.
While longer rods do give you more leverage in fighting the fish, I feel as though there's a maximum point to this principle when it comes to kayak fishing. Different to fighting fish on boat and land, you also have to maintain your balance on the yak while fighting the fish. Additionally, as you are in a seated position, the maximum leverage you can apply is also limited. Hence why I feel as though 7ft is the maximum length.
If you are dropping a bait/livie under a heavy sinker, any rod that can support the weight and is between 6-7ft long will do.
With regards to jigging, I currently use an Abu Garcia Veritas 3.0 spin jig PE 3-5 matched with fin nor LT 80 spooled with PE 5 braid. Why PE 3-5? I prefer a more mechanical jigging motion when going for kingfish. Also, depending on depths, currents etc, the weight of my jigs will also vary (from 60grams to 160grams +). The weight of the reel is abit heavy but I don't mind as i've gotten use to it. It's recommended that you get a rod that is specific to jigging. My thoughts are that jigging rods are designed to work heavier jigs and impart the desired action. I won't get into rods designed for slow pitch jigging as that's a different topic.
I think i recall reading that you have a pair of slammer 3 in the 10500 size? If that's the case, finding the right rod to suit the size of your reel may be abit of a challenge. Of course, if you could, i would suggest buying a jigging rod and a new reel to match. There are some on the market that won't hurt the wallet but also are quite good. Being honest, I think your arms will get tired very quickly if you tried to jig with a 10500 slammer 3. My opinion is that it would be better to save some money, do some research on what is available within your budget and progressively acquire the gear that you need rather than making any impulsive purchases only to regret them.
If you are curious, I would take normally 3-4 rods out on my yak. 1 sabiki rod. 1 soft plastic rod. 1 live bait or slow jig rod and 1 heavier jigging rod. Lately though, I haven't been fishing with live baits and would take my jigging and soft plastic rods.
Happy to answer any questions you have.