I work with HITI frequently (my
paper referred to it as NAVI). No matter how you execute your editing (i.e. HDR, NHEJ, NAVI/HITI) it is heavily dependent on the cell type and nuclease/guide-RNA efficiency. If you have a crappy guide, you're going to have a bad time no matter what. As for other, perhaps less obvious, tips that might not be discussed in the paper:
1. Whenever integration is the goal, be sure to include masked regions of the genome during your off-target analysis... you will likely be sorry if you don't.
2. If you linearize your vector and genomic locus by using the same gRNA, you may hurt your efficiency as there is much greater chance for target site regeneration upon integration.
3. If you are using selection, do a kill curve and use the lowest dose possible. Don't just use what your labmates say works best. Your intended outcome is not hundreds of plasmids, each expressing PuroR... It is one or two single alleles, now in a genomic context where expression patterns may not be ideal. This may affect the concentration of selection agent that the cells are able to withstand. I also generally wait about three days before applying selection. Of course, multiple passages help ensure that you are not merely selecting for cells with the original vector, as well.
I know some people remain sceptical, but I find it can really work well for certain applications and it's super easy to try. Good luck!
-Alex