Hi Jay,
I know how you feel, its a frustration, to have all the tools but not be able to use them. I would like to share to you an exercise that helped me.
As the same as all the previous post, the skill of playing the melody line and bass line is essential for you to decide which notes should be inserted within (which in turn completes the chord).
As the same as your question: Which chords should be used?
The good news is you already know how to solve half of the problem

since you are able to play the melody and the base line. The 'Base and Melody' pair that you play already determined the chord that you should/can play. You will appreciate and understand this more once you are able to 'spell-out' the notes of a chord in your head.
One effective way to learn the chords is to systematically introduce to your fingers and ears the notes that should be inserted within a baseline and the melody line that will complete the chord. The exercise below is very tedious, and very long, but rewarding so please bare with my explanation.
I Memorize this sequence of notes (just movements in fourths).
- A - D - G - C - F - Bb - Eb - Ab - Db - Gb(or F#) - B - E
II. In every melody line/note you are able to pair it with any of the 12 notes/tones as the base line
- Let us start with with your right hand playing an A note (which act as our 'melody' note
- with your pedal or left hand base, use the sequence above ( I. movement in fourths) as the 'base' note
- LH or pedal/RH (see pattern below)
- A / A
- D / A
- G / A
- C / A
- F / A
- Bb/A
- Eb/A
- Ab/A
- Db/A
- Gb/A
- B /A
- E /A
III Decide the chord based on the Base and Melody note
- The base note will act as the 'root' of your chord
- What is the relation ship of the melody note (or top note) with respect to the chord
- A/A = since the base note is A, think of what A chord has the A note as melody
- The answer is A major A minor (actually all of the possible A chords ), Now, insert the missing notes to complete the chord having the top note and base note as A (for major you insert C# and E in beween the bass note and melody note)
- Next lets move to D as the Bass note and A 'still' as the melody note
- If D is the base then think of what D chord has an 'A' note in it
- The answer is D major and D minor (because you need A as the 5th note to complete the chord)
- Play the D note in your base and your A note as the melody and insert the note needed to make a D major chord(F#) or D minor chord (Fm)
- Now that you got the idea, below are the remaining 10 base notes with chords
- G / A play Gadd9 with G as base and A as melody
- C / A play C13 with C as base and A as melody
- F / A play F major with F as base and A as melody
- Bb/A play BbM7 with Bb as base and A as melody
- Eb/A play Eb dim with Eb as base and A (or Bbb) as melody
- Ab/A play Ab b9 with Ab as base and A (or Bbb) as melody
- Db/A play Db aug with Db as base and A as melody
- Gb/A play Gb min with Gb as base and A (or Bbb) as melody(
- B /A play B7 with B as base and A as melody
- E /A play E11 with E as base and A as melody
- Please note that there are more chords possible in any of the 12 combination (such as the last example E/A, it can be also played as Eminor11)
IV Do this exercise with all 12 melody notes (sequentially A,A#/Bb,B,C,ect or in fourths A, D , G , C)
The benefits of this exercise.
- You have introduced to your ears and fingers atleast 12 new chords that can work a melody note
- You will improve your 'thinking in fourths'
- You have increased your patience (this excercise is long and tedious!)
- You will improve your ability to spell out the chords you are using
I hope this will help you as it has helped me, God bless you on your efforts! And may His Name be glorified.