That sounds like an overly complicated setup with far more pumps than it should need. Or else you said pump when you meant tank in two places, actually, re-reading it.
In short, you can have as many pressure tanks as you like. Locating them closer to the point of use (the house) would be helpful, to a limited extent. That limited extent is the "effective volume" of the pressure tank at the house - while it's got pressure, you get better pressure at the house. As soon as it runs out of water and you become dependent on the pump, the pressure loss of the 300 feet of 1" PVC to the house comes into play, until you slow down your water use to the point where the pressure tank at the house fills up again.
If you do not change the setpoint pressure, the peak water pressure in the house will not be affected at all. Once the pressure tank at the house is depleted, the pressure will be the same as it is now. If you have a pressure gauge at the house now (or can add one) it might be useful to know the pressure at the house when "loads of interest" (showers, say) are drawing water.
Most pump controls can be altered to have a higher setpoint pressure, and most well pumps will provide that, within reason. General recommendations are to stay below 80 PSI - but if you are now running your pump on at 20 off at 40 (a typical default) you could turn it up to on at 30 off at 50, or on at 40 off at 60 - you will need to adjust your pressure tank (and any you may choose to add) for the higher pressure, particularly if they are bladder-type tanks - with the system drained, a bladder tank should typically be 2 PSI less than the low water pressure setpoint (ie, 18, 28, or 38 for the three ranges I've just given) and you may need additional pressure tank volume (because the effective volume of water a pressure tank can hold goes down as the system pressure goes up.) So, you can probably get more pressure without another pump, and possibly without another tank, but we'd need more details of what your system is doing now to know that for certain.
Unless your water use is extreme, 300 feet of 1" PVC pipe should not have a lot of effect on the pressure - at 5 gallons per minute, about 2.2 PSI - at 10GPM, 8.2PSI, 15 GPM, 17.4 psi
If you are fundamentally opposed to (or trying to avoid paying taxes on) an aboveground structure, you could bury a vault to put at least a small pressure tank in. With use of a "constant pressure valve" or a variable-speed "constant pressure pump" you can get away with quite a small pressure tank (2-5 gallons) but you really can't run a pump without any pressure tank, at least not remotely efficiently (you could, I suppose, put a pressure-relief valve in the line at the top of the well, and run without a pressure tank - the excess pressure would recycle water down the well, but that's a terrible waste of power...)
If you really need water in the winter, bury the whole thing below frost line - one common method is to use 4 or 6 foot diameter concrete well tile (as used for shallow dug wells) placed over/around the drilled well casing to provide the frost-free vault - you can insulate the top and sides for better effectiveness. While you have a backhoe in to dig for that and the power line, dig some trenches below frost line to where you want to have hose spigots, and put "frost-free hydrants" at each one (they have a valve at the bottom, and leak away the water in the upright pipe between uses.) Might as well have the backhoe dig 100 holes for trees while you have it, too.
If not fundamentally opposed to a structure, an aboveground structure (small toolshed for the orchard) above the wellhead might be a less expensive approach, unless the local taxing authority makes it an expensive approach after all (that can happen, and is best to be aware of when deciding.) The area with the pressure tank can be heavily insulated and electrically heated to 45F or so if you really need water to hoses in freezing weather, or you can drain the whole system in the fall and start it up again in the spring if you don't really need to use water from hoses in the winter.
Best Answer
Your recovery rate is the problem. A larger water heater will still need to be refilled as the water is removed so you will run out of pressure in about the same amount of time.
A water tank of several hundred gallons added to your system with a pump may help, but in the summer you may have a lower water table and not have water at all.
In some areas there are companies that rent tanks/pumps that your system can pump into. If you do go dry they can be filled by a water truck. Very expensive water to go that route but it may be an option until you can have a new well drilled.
Just a word of warning drilling deeper doesn’t always work; close to the coast you may hit salt water going deep, other areas can have arsenic / sulfur that makes the well unusable. Make sure to get a good driller that knows your specific area and you may want to talk to a certified water tester (the ones that check for flow and contamination) as they know the depths and problems in the area.