There is a parameter 'Number of elements' (example: 'Nelem' in the link provided).
If the chosen number of elements is too low, then you'd expect to see holes in the bandwidth; especially at the low end where the percentage bandwidth is worst. For example, if somebody designed a log periodic antenna with only two or three groups of elements (an extreme example to make the point clear), then you wouldn't expect it to work very well. As a general rule, using a larger number of elements should assist in smoothing things out over the bandwidth.
If you're using a log periodic antenna, then you shouldn't bother removing elements to eliminate bandwidth.
You might also be able to tweak the element lengths to move things around a bit. If there's a reflection at 700 MHz, then adjust things so that there's a pair of elements accepting power at that frequency.
Thing is, you're trying to achieve a bit higher than 4:1 bandwidth (450 - 1900 MHz). That might be a stretch. If you can't make it work, then you might have to find a parallel arrangement of two antennas, each covering their own bandwidth.
Disclaimer: I've never designed a log periodic antenna, so this is all based on other somewhat related experience.