IMO, you may have missed the ammonia spike, but CLEARLY you had ammonia as you have the next products of bacterial conversion - nitrite and nitrate.
A cycling tank should be tested (ideally daily - but who has the $$) very frequently. At least every couple of days...regardless of day 1 or day 30.
Tanks without LR often cycle in 4-6 weeks; with LR it can be shortened considerably, to the point where it becomes a concern on whether anything has happened. At this point, it would not hurt, IMO, to challenge the tank.
LR, even in small amounts, would have the "starter" bacteria we are looking for to convert ammonia to nitrite. The cycling process is the amount of time it takes for the population of those bacteria to reach levels where it can "eat" the available ammonia. We want lots of ammonia, because we want lots of bacteria. Ditto then for bacteria that "feed on" nitrite, and finally nitrate (which in many cases simply accumulates and is not broken down further due to the need for anaerobic conditions). You can add additional bacteria if you wish, but it will still take time for the bacteria to reproduce. But no worries, LR provides plenty to start with.
IMO, it doesn't really hurt to push the tank again...probably, you won't really see an ammonia spike. If you do, then it was a good idea!
Theoretically, you could have had more ammonia "eating" bacteria and didn't see too much of a spike, but there may be a bit of a backup as the bacteria converting nitrite build their population size. If the tank "stalled" at any phase (ammonia or nitrite), then I would consider the addition of more LR, or bacteria culture in a bottle. But because you have nitrate production, this indicates that the cycle is progressing, IMO.
What sort of test kits do you use? I am wondering if your nitrates really are that high (very high coming out of a cycle...lots of water changes may be in store before addition of fish).