Not strictly engraving, but rather notation question

[MichelRE]

I am having difficulty finding the right words for a tempo change in one of my latest scores.

context:
cadenza-like passage, between the soloist and a flute solo.
the material is written so that it is completely rubato/free, with each instrument free to enter at or after the end of the other's phrases (it's sort of question/answer format).
these are relatively longish measures, the passage is in 6/4, and most of the notes are 16ths or faster values.

difficulty
there are four measures that start very slowly, but accel. poco a poco
the four measures are the passage that is rubato/free.

Once those four measures are done, there is a new, faster tempo (it started at ca. = 48, and this new tempo is now a strict = 76)

I need to clearly mark that the first passage gradually speeds up, and is also completely free (not quite aleatoric, though maybe rhythmically?) then attains a new faster tempo that is now strictly in tempo (or else it is impossible for the two musicians to play together).

I had originally written accel poco a poco, for the first four measures, then at the new tempo, più mosso, ma tempo giusto ( = 76)

however, I was told this was somewhat wonky Italian.
Please, I need suggestions on how to handle this excerpt.
It's frustrating because it's such a short passage in a 25-minute long work!!

[OCTO]

Why not to omit the tempo text (yet using accelerando) and write =48 accel. =76

The next tempo is in any case più mosso.

[MichelRE]

the issue here is that from the start of the accel passage at measure 162, there is no real "battuta", it's quite free. as long as it gradually speeds up.
but then, when it hits measure 166, the tempo is now faster, but more importantly, it is no longer "free" but in strict tempo at this new tempo.

those first four measures, which speed up gradually, are marked rubato (I'm considering adding "molto" or just outright changing it to "très librement", in French).

[John Ruggero]

Molto rubato = ca. 48

accel.

Tempo giusto = 76

[OCTO]

but in strict tempo at this new tempo.

tempo preciso =76 ?

[MichelRE]

Molto rubato = ca. 48

accel.

Tempo giusto = 76

that's very close to what I ended up doing. I included "più mosso" before the tempo giusto.

because of the nature of the music (just looking at the notes one wouldn't automatically assume that there is a sudden change in the tempo, or that the accel isn't continuing past that point) I felt it important to specify that there was a new tempo (più mosso) and that from this point on it was "tempo giusto".

[Harpsichordmaker]

I had originally written accel poco a poco, for the first four measures, then at the new tempo, più mosso, ma tempo giusto ( = 76)

however, I was told this was somewhat wonky Italian.

I have no suggestion for your question but as an Italian I can only say that's perfectly correct Italian. I could only suggest putting a dot after "accel": accel., as it obviously is a shortening for accelerando.

[MichelRE]

thank-you Harpsichordmaker. I think the accel. in the score has the dot, it may have been a mistype on my part here in the post.

I'm glad to know that the indication for the new tempo is actually correct Italian.