Its unlikely you will get as good match on 40 m as you have on 20 m unless you double the height agl. The RSGB Handbook used to have a nice graph of feed resistance vs height.
Google tells me that a 7 MHz dipole at 20 m agl will have a feed resistance of 71 ohms resistive and an SWR of 1.4:1 for 50 ohm coax. Lowering this dipole to 8 m agl oddly gives the same resistance but adds 56 ohms of inductive reactance, spoiling the SWR. (2.6:1) Dropping it further to 4 m pulls the resistance down to 23 ohms with 39 ohms of inductive reactance (3.6:1). Adjusting the length for best SWR at your intended height will yield the best results without a tuner or other matching. Which might be where you are now.
SOTABeams uses thin coax and thin wire that have some inbuilt losses and hence appear as better matched at any height. Ground resistance is of course quite variable.
In my more recent SOTA activations I always had an ATU and usually a 5 MHz doublet fed with 300 ohm ribbon. I figured if I needed an ATU I might as well give up on resonant half waves and go for the smallest antenna that will work well on 80 m. I can QSY to any frequency (3 - 55 MHz) in 15 seconds. Lazy.
Tony VK3CAT has always used a double 5/8 for 20 m with 300 ohm feed to his KX2 to cover the same range. Its taken me a decade to come to a similar arrangement,
Now I’m using something else but its not for SOTA.