if you take a 6 second round and 90ft movement, with a top sprinter needing less than 10 seconds on 100 metres (300 ft.)? That does not sound so out of realism for me tbh.
The world record for 1000 m is 2min11 seconds = 131 seconds.
Let us see how far continued dashing for 2min 11 seconds takes us: 30 ft. x 131/6 = 30 * 21 = 630 ft that's 210m. Not so impressive and not even amateur sports league. with a con of 20 you would not need make checks for the first 20 dashes if I interpret
@UngeheuerLich right (no time to look it up now)
That also really does not sound superhuman to me.
Actually, it is off IMO. (and FWIW, any world record is pretty superhuman to me LOL!

)
90 ft/round is 15 ft/second or 21.9 sec for a 100-meter, which is really slow actually for running (i.e. move + double dash). The world record 100-meter holder would be moving 205 feet / round (a speed of nearly 70). If you assume Bolt is an 18th-level Monk with Mobility, using step of the wind twice, that would do it. Personally, I am okay with that myself I suppose...
Now, your example. (I am not sure what you are doing with some of your numbers...) Anyway, 1000 m = 3281 ft.
3281 ft/ 131 seconds = 25 ft / second or 150 ft/ round (25 x 6 seconds), which would be a speed of 50 (150 / 3 for move and double-dash).
50 is MUCH higher than 30, so I would consider
that impressive. Maybe a Human 2nd-level Monk/ 2nd-level Rogue with Mobility? Ok, so getting that speed is not hard I suppose...
Also,
@UngeheuerLich must be suggesting a house-rule (a good one IMO), but sticking to the RAW...
With a CON 20, you don't make any checks for 8 rounds. After 5 rounds (on average), you would be making checks with disadvantage, so you would fail another check in about 3 rounds (again, on average). Meaning after 16 rounds, your speed would be half. At 90 ft/round, that is only 1440 feet, less than half of the 1000-meters (3281 feet).
So, let's assume a speed 50 (however you get it). Monk won't work, because you would run out of Ki, so let's go with the Human Monk/Rogue 2/2.

With a CON 20, such a character would fail their 4th check around round 22, just as they finished the race. So, plausible I guess.
But it means in another 3 rounds (barely 2.5 minutes), their speed would be 0 and done. So, the 38 rounds for the world-record mile would pretty much never happen (speed would be about 45 as well even if it could happen in RAW).
Now, all of this is with a CON 20 (not normal at all) and being about to double-dash a lot. It also assumes a rogue's double-dash doesn't count as two uses, but it should really, making all of this even more extreme.
FWIW, I ran a 11.5-sec 100-meter and a 4:52 minute mile when I competed in T&F.
For that 100-meter, my speed would have to be over 57, assuming I was moving and doube-dashing.
That mile was a speed total of over 108 feet per round for over 48 rounds. I would have had my speed reduced to 0 long before I finished and my CON was certainly not 20 (maybe 14 I would guess since I was running a lot).
Finally, this assumes you don't want a game where your PCs can do things beyond what people can do IRL. IME, a lot of players want PCs who can do more than is possible IRL.