Those JBL's retail for $275! right on your price range, and you can get them for 1/3 of the price on sale
When you bi amp them, either set, even the ID's, not sure if you tried them active or not, you have more power and more dynamic sound and getting loud is not necessary unless you want to hear your car from a block way with the windows open.
I don't know how much is the real power of the PPI amp, the 150x4 is usually at 14.4v, not realistic to me. The real power is at 12.6Volts.
With either set, you can bridge the PPI channels to give the mids at least close to 200W, and the tweeters driven with the HU or a small amp.
If that does not solve your issue of loud SQ, then you may want to seek a 3 way front and sub and that will ask for a DSP.
Those silver flutes and those tweeters are a good 2 way system for a 2 way active. I have set of Hertz HSK tweeters I may be interested in selling, the HT25's the newer ones with the black and silver lines grills. And those get as loud as you can stand them.