Next, when making a pair of single vision glasses that can see distance and near might only solve your eye strain issue temporarily. Like what you are experiencing now, distance is starting to get worst due to compensating for your near. What you might need at this point of time is, depending on your age, perhaps a progressive-to see distance/intermediate(computer)/near. But take not, it is impossible to get the best of all 3 worlds. Usually we have to choose between 2 of the above 3.
Next if you are between 30-40 maybe you can consider using antifatigue lenses whereby the TOP segment is catered for your full distance whereas the lower area power is gradually reduced so as to allow you to read at near comfortably. The power of the lenses can be adjusted depend on the type of lenses you get.
FYI, an anti fatigue lenses, can be useful as you can take it as a stepping stone to transit over to a progressive lenses in future. So it be easier for you to get more adapted to a progressive lens infuture.
Also lenses by themselves usually can correct up to -2D of astigmatism and more if the lenses are more customised so I am not so sure what do you mean that the astig not too high so not added into the lenses. E.g astig -0.25? -0.50? As if you have astig of -0.75 you can generally feel that it affects your vision esp at night when you look at road sign boards and see halos/flares when seeing traffic lights and such.
Hope this helped and feel free to ask/correct me if I make any mistake so I can learn myself too. Thanks!