In general, you need decent processing power to change pitch with low latency. I’ve noticed that it’s not always easy to find out latency data about gear.
Perhaps, it’s worth trying something more expensive. In theory, if something costs more it should have faster processors and lower latency. Of course, it does not always work out that way. So, you have to try in store or with a return policy to find out.
My Virtual Jeff digital whammy does pitch shifting in half steps. It can do a full octave up or two octaves down. The latency is low but the price is high.
Also, if you take a note or chord and change it to a dramatically lower pitch, I think you tend to get more latency because it has to slow things down to create the lower frequencies. So, I think even a high dollar unit is going to have some noticeable latency in an extreme change from high to low. Again, my Virtual Jeff has low latency even in that scenario but it was not cheap even discounted during a Black Friday sale.