Water Pressure Pump Location

We would like to increase the hot water pressure in our home to increase the flow rate in our upstairs shower.

We are in California on city water (no well). I spoke with the water company and they said we are on a gravity fed system and it is not possible for them to increase the water pressure. They calculated the water pressure at our tap at 38-43 PSI.

I have done the following:

• Pressure regulator valve (located near hose bib in front of house before water pipe enters the home) is wide open (maxed out at 80 PSI).
• Water pressure at hose bib in front of house, after the PRV, before entering the house is 38-40 PSI.
• Water pressure at cold water inlet to the tank hot water heater is also 38-40 PSI.
• I bypassed the water heater by connecting the cold water inlet flex hose to the hot water pipe going into the house and the water flow was the same at the upstairs shower. This rules out an issue with the water heater.
• Removed shower head and observed same slow flow rate. It’s not the shower head.
• Checked aerators at faucets and did not find any significant deposits.

I am considering installing a water pressure pump (like SEAFLO 33-Series or similar, or a more expensive Davey brand pump). Some questions:

1. Would such a pump improve our hot water pressure for our home?
2. Do I need a water holding tank for such a pump, or can it work without it?
3. If I’m just trying to increase the hot water pressure, where should I install it – before the cold water inlet to the hot water tank, or after the hot water outlet of the water tank?
4. What type of lifespan should I expect from these pumps?