Voltage drop is caused by internal resistance
Using batteries you will always experience a voltage drop when drawing significant currents, due to the internal resistance of the battery. This can be thought of as a resistor that is always in series with the battery, and consumes energy depending on the current drawn from the battery.
It’s the main reason batteries appear to have lower capacity for high current draws, and higher capacity for low current draws. It also accounts for battery heating, and is one of the ways a battery may damage itself.
Internal resistance depends on the battery
Most general-purpose SLA batteries should have 100 mΩ (0.1 ohms) or less of internal resistance when new. A battery that has a higher internal resistance may be damaged, and will not be as useful as a battery with low internal resistance. It may also be designed that way for high capacity, low current draw applications. You should be able to find the intended internal resistance from the manufacturer’s data sheet. If your cells have a very different internal resistance they may be damaged.
As batteries go, though, 100 mΩ is a lot of internal resistance. At a 20 A current draw you will see up to a 2 V drop. You’ve already done well to put the two batteries in parallel: each will see 1/2 the current, leaving you with a more reasonable 1 V drop when you transmit.
How to measure internal resistance
You can measure the internal resistance of your batteries by watching the voltage drop at a 1 A load and a 10 A load. The internal resistance will be the same on both loads. So take the two currents and the two voltage drops, and solve for the one resistance common to both. If your SLAs have resistances above 100 mΩ, you may want to put them into a lower demand job and replace them with newer batteries for your radio use.
How to obtain lower internal resistance
Putting cells in parallel, as you’ve done, is one method that reduces the overall internal resistance of the pack. You could go further and use four 7.5 AH batteries to get even lower internal resistance, for instance.
You can purchase better SLA batteries with lower internal resistance, but there are generally a host of tradeoffs you make depending on the capacity, lifetime, power density, and other factors that should be weighing into your decision. If this is for a specific use, consider asking a new question with your desired use case and we may be able to recommend a few specific battery types and sizes that should better meet your needs.
Generally speaking you might want to focus on SLA batteries meant for high rate discharge applications, such as UPS batteries. These typically have an internal resistance at or below 10 mΩ, which would give you a 0.2 V drop for a single cell driving your 20 A load. Note that even with such batteries, you still have a voltage drop; what you need to determine is how much voltage drop is acceptable, and then choose the batteries that meet that requirement and any other requirements you may have.
You might also want to look into super-capacitors if your transmissions are generally short. By using batteries and super-capacitors in parallel you can reduce the instantaneous current draw on the batteries during short transmissions. This will have the additional benefit of reducing the effect of the internal resistance, giving you more capacity from the battery, and may extend the life of your batteries somewhat.
If voltage drop is unacceptable, you may want to look into voltage regulators that will take the battery power and provide a stable voltage regardless of the load. For radio use this is generally overkill — most radios work well with even a 2-3 V drop, and significant energy is lost in the conversion, so it’s only recommended for special applications.