For this tune, the most important is to have the right bass progression that you already have. You're on D minor all the way long for this two first measures, but there's a strong bass movement very important for the "sentimental" feeling of the tune.
I already play this tune and I don't choose the same notes on the high bass register. Maybe you should try to play on the left hand a more opened voicing with 7th/6th. Try to play for the two first measures :
- D (bass) plus F and C
- Db (bass) plus F and C
- C (bass) plus D and A
- B (bass) plus D and A
For me, there is a nice movement, having a bass movement changing twice faster than the upper register of the chord for the left hand who remains the same the whole first measure and then changing and remaining the same for the whole second measure (is it understanble...? I don't think...)