The problem (difficult to solve with EQ) with "Bronze/Brass" Wound Acoustic guitar strings with magnetic pickups is the windings are not magnetic and therefore the magnets in your sound hole magnetic pick up can only detect the steel core deep inside the winding. Electric guitar strings are nickel wound and the nickel windings respond to the magnets in your pickup.
The larger diameter bass acoustic strings (E and A) will be less responsive than a wound D or G string because there is more material insulating the steel core from the magnets. The plain steel strings on electric and acoustic sets are the same material and equally responsive to a magnetic pickup.
On the acoustic guitar I play that uses a magnetic soundhole pickup, the best solution I found was using nickel flat wound electric strings for my wound strings. I found the flat wound strings sounded more like an acoustic guitar (mellower) which was the sound I was going for.
Another solution (besides using electric guitar strings) is Zebra Strings by DR DR Website. The Zebra strings are alternately wound in both phosphor bronze and nickel (giving them a striped appearance) and therefore respond to magnetic pickups while retaining a brighter acoustic tone. They are marketed as a string that is both Acoustic AND Electric - because they will work for either type guitar.
They offer 7 different sets with various gauge combinations. Pictured below is a box of what they call "Custom Light".
An alternative solution (if you don't want to solve the issue by string selection) is to add either an internal or external microphone based pickup, or a soundboard transducer pickup in addition to your magnetic soundhole pickup. These type pickups are not dependant on the magnetic properties of your strings.
Soundboard Transducer Pickups attach to the guitar top and sense the vibrations of the top. They can be permanently mounted (check out the K & K Pure Mini K & K Webstite) or can be found in a removable external version. The K & K Hotspot (pictured below) attaches with removable adhesive (I would attach the input to my strap) on the guitar soundboard. You can get different tones by moving it to different areas on the guitar top.
Hotspot External Soundboard Transducer Pickup
If you add either a Guitar Mounted Mic Pickup or Soundboard Transducer, you could then use an A/B/Y footswitch to choose either your magnetic soundhole pickup, your alternate pickup or blend them together to get various sounds and tones to fit the musical situation.