The matter of LLT excursion below tuning has been a hot topic for some time - mainly because people who don't have any experience with one have creative imaginations
(by no means you, I am referring to old debates on other forums). Simply stated,
nobody who has a built a LLT has ever experienced any bottoming due to below tuning playback of real material. You ca find a detailed explanation why in my LLT Explained thread, but to sum it up, most electronics start roling off in the teens or single digits. Add up the rolloff of your dvd player, processor, amplifier, and an EQ unit if you have one in the chain, and you gain protection from the lowest of lows. Additionally, the levels required for your to reach overexcursion at such low frequencies are rarely if ever reached. Also, xmax is a parameter in which the excursion is essentially "behaved", but there is also xmech, the physcial travel limits of the suspension, and in high excursion drivers, it can be quite large, 40mm+. Lastly, if Ilkka's experience translates well to other high excursion drivers, then the suspension itself will gradually start to resist extreme movement beyond xmax. Combine all these things and a few others, and you are safe from having to worry about bottoming a LLT below tuning with actual material.
If you keep increasing the level on somethng like a 5hz sine wave though, then yeah, you will likely bottom and damage your driver assuming you don't fry the voice coil first.
Ok, budget of $1000-$1500. Subtract $300-$400 to start with for the amp, and another $200 for enclosure materials. Assuming you have the space for it, you should be able to go with your choice of dual RL-p18s, Q18s, or, if you want to save the most, Mach5 IXL18s.