"How can fitting nuclear warheads on TLAMS onto boats already capable of firing TLAMS be more expensive than designing, developing, building, testing etc of a brand new SSBN boat and missile system?"
Many reasons! Firstly its not an existing weapon system, it'd be an entirely new system. We'd have to design and field from scratch the warhead, the missile system, the support network and so on. Thats assuming the US sells us TLAM if they knew we'd stick a nuclear warhead on it, and that we can do so under counterproliferation treaties.
I'm trying hard not to sound patronising or one track record here, but it really isn't cheaper. I know it comes up a lot, but I can assure you that vast amounts of research has been done on this over many years, and they always reach the same conclusion. To deliver the effect we want at a minimal cost, the SSBN is the only answer that is credible.
Nuclear TLAM is great if you want to give your opponent several hours advance warning of a strike and also mean you can't use any form of cruise missile against them for other purposes without passing the escalation threshold.
Additionally, one minor but critical point to consider. SSBNs are designed to sit there silently and wait for orders to be received. The most critical and vital part of a deterrent isn't arguably the warheads, its the Command and Control and Communications element to ensure that if the PM requests a nuclear strike, CDS can order one (a critical distinction). The C3 package is exceptionally complex, requires a lot of kit and isn't something you could easily change without incurring a lot of expensive rebuilding (if you do some googling you can fairly easily see some of the sites we require to this day to keep the nuclear firing chain in place). You also need to refit the submarines to carry the comms suite to do this - this is not as simple as putting some radios into a hull, and would probably require an entirely new design to be built.
In other words you're building a new design weapon, a new design warhead, a new design submarine, a new design C3I battle management system and a lot of other stuff to, and in return you reduce your tactical options against most opponents and spend a lot more money to do less than you could do before. Why does this make sense?