Cheap two way crossovers for sub/wall speaker outdoors system

I have two outdoors zones, one with a pair of Polk Atrium 5 and one one with a pair of Bose 251 Environmental. Neither of them have enough bass for me, power metal needs power and prog metal needs the six string bass to sound out! 😉 My plan is this:

Make a bass system that I can move where I am spending the afternoon (it all depens on the wind, one side is great for northern and eastern winds, the othe one is for southern winds. Western wind is a toss-up) and store in the shed when I'm not using it. I will repurpose a 10" JBL subwoofer box that I have from an earlier car (last ten years my cars have had those built-in audio systems that I haven't bothered to mod) and a car amp I have laying around for that, and a 220V-12V power supply (which I have on order, 25 ampere and weather proof). That will be fed by the main amp's line output for the zone. The car amp has built-in crossover so that only low frequencies will be sent to the subwoofer. So far no problem.

The problem comes when I want to crank up the bass and volume. I need to stop the lower frequencies (from 125 Hz and down, maybe?) from reaching the Polk and Bose speakers, or I will blow them. So I want to use a crossover on each speaker. Complicating things is that I can't have the crossovers indoors, because when I have a party I bring out a pair of 12" Wharfedale Titan 12 PA speakers, and they can take care of anything my amp can throw at them, so I don't want to cut the low frequencies from the amp and out. When they are out, I use relays to route the amp to them instead of to the Bose and Polk speakers. So the crossovers have to be outside, and they can't be that expensive, in case humitidy ever gets into the box. Oh, and there is no sub out on the zones I'm using (zone 2 and 3 on a Yamaha RX-V 2067).

So is there something that could work for instance on Aliexpress or eBay, that isn't all that expensive, but still won't degrade the sound more than the speakers do? They are pretty good, not high-end, but few outdoors speakers are. So that means that the crossovers would have to be able to put out sound in the same class.
 
An active solution would be the obvious one to recommend.

Are either of these speakers sealed? Your specific situation has me thinking about the capacitor bass boost method where a single capacitor changes the bass rolloff to third order while boosting near the rolloff and cutting the lower bass.
 
Thanks for answering! Active is impossible, even if it would be preferable. The audio in is HDMI, and there are nowhere to access an analogue signal for those speakers. And a digital solution is impossible too, that would add delay, and there is overlap between the audio in the living room and the audio outside. But I have found a possible solution to the waterproof thing by moving the sub amp indoors and having a separate sub cable going to the spot where I am going to put that, so that I can have the crossovers indoors as well.

The outdoors speakers are all sealed too. I think a two way crossover for the speakers is the only possible solution, or more precise (I should have thought about that in the first post) a high pass filter that filters around 125 Hz.
 
I may have found another solution... Turns out I have another car power amp that I had forgotten all about, a four channel Planet Audio with a built-in active crossover, where I can bridge two channels for the sub. With an Antminer 1600W psu (that should be around 130 amps in 12V), which I can pick up for cheap, that one should be easy to drive from the line out on the receiver. I will try that first and see what happens.