I am currently using a 'phage integrase' system to insert my gene of interest into P. putida and it is definitely a seamless process with high efficiency so I highly recommend it!
As for your question, the method through which we integrate the gene of interest using the phage integrase system is simpler than you think. We do not change the payload of a bacteriophage. We simply electroporate with two plasmids, one that expresses the BxB1 integrase and another plasmid that has our gene of interest that we want to integrate into the genome of P. putida. This integration is highly efficient, and it operates through a serine recombinase that recognizes specific attP and attB sequences in the plasmid that contains my gene of interest and native genome of my engineered strain. This method is significantly more efficient for engineering certain strains (typically non-model organisms) for genome integration purposes.
References for additional information on the system for your review:
Here is a paper that describes how we use the phage integrase system to effectively edit the genome.
Here is the paper that discovered and characterized the mechanism this system operates through.