I listened those first few songs you posted Hello H2O; sounds great, and it's impressive how well you're playing already!
Those old jazz songs aren't always tuned exactly to 440hz, so you may have to adjust little bit your bass guitar's tuning by ear, depending on the song you are playing. But it's the timing and rhythm that counts the most in this genre!
D minor is relative minor of F major key (their scales F-ionian and D-aeolian share the exact same notes), so that's why you got the result from key finders, but the correct key for 'Have You Met Miss Jones' is indeed F major.
When looking for the correct key signature, you can start by searching V (dominant) - I (tonic) chord change, in this case C7 - Fmaj7. If you have the sheet music available, then start by looking at the key signature, then find clues is the key in major or its relative minor.
Look for the important places first, e.g what are the first and last chords. In 'Miss Jones' you can notice how there's C7 always at the end of every fourth bar in the section A.
It's basically the classic I-VI-II-V chord changes with some chord substitutions in the mix (for example the second chord F#dim7 is basically D7 chord with major third on the bass).
The B part of the song is bit more advanced when finding the key, this type of harmony was actually later popularized (and further developed) by John Coltrane. You can think of it as transposing between three separate key signatures, which are structured to be major third apart from each other: Bb major, Gb major, and D major (augmented triad). Then you can notice how each of them are preceded by the II-V chord:
Cm7 (II) F7 (V) Bbmaj7 (I).
Abm7 (II) Db7 (V) Gbmaj7 (I)
Em7 (II) A7 (V) Dmaj7 (I)
Then it returns back to the more traditional tonal harmony. By the way, one good example of a song in both major and its relative minor key is 'Georgia On My Mind'. Section A of the song is in G major, but the B-section moves into its relative minor key of Em. This is preceded by V dominant chord B7 (around 1:15 in the recording below).
You can now apply the above for this, look in which of them you'll see the dominant chord (V7) in the key of Eb. Hope this helps!