Installing a permeate pump on a manifold-style RO system
I'm not sure if I understand your drawing, but I think you're saying you want to add a pump on the product side to keep pressure above 42 psi. I don't believe this is going to work due to the shut off valves. I'm pretty sure that if you attempt this your RO will never turn on.  

Here is how the ASV (automatic shut off valve)  works. The feed water is connected to the ASV on the indicated port, which goes to the membrane element.   Some are in and out in the same side, some are straight thru.  

The product water somewhere after the check valve is hooked up to the other side. Inside is a diaphragm valve. When your tank is empty, this valve is forced open by the incoming pressure (for simplicity let's say 60psi). The ASV pressure is specified in ratios but a good one is 2/3.  So this means that when the product water reached 40psi the feed water will be shut off to the membrane. And of course the product water doesn't flow backwards due to the check valve. The physics of how this is done might be explained later. But that's how those work.   It should make sense why you can't just put a pump on the product water. You also just can't add air to the tank for a higher faucet pressure either.  The limiting factor is that 3 in our ASV 2/3 ratio.

But is there a solution: raise the feed pressure.

Membranes operate better on high pressure. They tend to last longer but more importantly its rejection rate is much higher than when run at line pressure.   But we have to get rid of our ASV, and substitute a couple of pressure switches; one high pressure switch for the product side and a low pressure switch for the feed side. The HP switch will turn the RO pump on and thus make water until it reaches its set pressure then turns the pump off and then stops making water.   The low pressure switch protects your pump in case your feed water pressure drops or if it gets no water at all.

What's the risk? Let's say your feed pressure is greatly lowered.  Maybe a fire in the neighborhood and the fire trucks are using all the water.  So your RO kicked off. But no big deal right.  Well after they removed their back flow preventer a bunch of contaminate was stirred up and plugged your pressure regulator. No water or low flow condition.

You don't notice and go to use your insta hot. It works fine, but all of a sudden you tank is empty and the heater burns up. This is a crazy example but you have to keep in mind that if something happens to the pump then your insta hot is in trouble.

What do I recommend?  Leave the insta hot on the soft water. And just use the RO for the faucet and icemaker.

Adding a pump is not all that uncommon the benefits are staggering but to retrofit one to a unit especially under counter had some major drawbacks: the pump will be noisy, and high pressure across old plastic spells flood.

The higher pressure switch had a range let's say 30-60psi but our tank pressure needs to be 28psi, so that the RO doesn't need to run very long to keep that switch closed.

Hope some of this helped.