I too was about to suggest a silenced Topre board as it gets a fair amounts of thumbs up in terms of silencing. D-I-Y silencing or otherwise factory fitted silencing. Until I saw the maximum price you want to pay for a keyboard. The only option again as suggested is to go for second hands and fit your own silencing on them if they don't have any silencing fitted.
Then the idea of fitting on silencers for the mechanical keyboard you currently own but then you said that emits a high pitched noise which is not something that you like.
You are pretty much limiting too much factors here, most mechanical boards as far as I know have metal parts that they use to actuate the key presses. These metal parts will make a sound, no matter how much silencing you want to put on them unless you want to go with some cheap membrane keyboard.
Topre has metal spring, ALPS, Cherry MX and Buckling Spring all have springs. Hushing the metal is not easy as people would know when metal hits metal in general it would create a sort of "ting" noise when they contact with each other.
If I were to be picky about what you wrote, you did not specify that you want a mechanical keyboard, that would allow me to give you at least two suggestions. One of them would be a touchscreen keyboard with the haptic feedback turned off. There will be no need for the keys to travel any sort of distance. Then there are those water resistant membrane keyboards, these are sealed pretty completely and chances are they won't make that much audible noise when used. Last but not least are those "holographic" keyboards, keyboards that uses laser to beam an image of a keyboard (at least the layout) onto an empty table. Again much like touchscreen keyboards, there is no need for a key to travel any sort of distance as there is essentially none. Typing on those holographic keyboards I can imagine would be as fun as tapping on any old regular desk without any sort of keyboard or anything.
Now, with that mentioned aside, $150 seems to be fairly restrictive for a mechanical keyboard with or without silencing pre-fitted. You could think outside the box for a bit and invest in some idea of making/buying a soundproof bag/box large enough for your keyboard and/or mouse to sit in. The more soundproof (including to the extreme point of where you have to use those "gloves" provided within the bag/box in order to type on the keyboard, etc.) the chances of keyboard emitting any sort of noise probably is the better.
Maybe something like this:
Then with whatever remaining amount of funds, consider putting soundproof foams, drilling hole in the back to allow the keyboard and/or mouse cable to go through. Any larger holes, consider sealing the rest up with either rubber grommit and/or putty mixture.
