Virgin Queen introduction

So, I was a day late pulling a batch of queen cells, and had several hatch while I was working. I had my nucs all made up so I ran around putting them in, some walking free, some just breaking out. I also took one over to another yard where I had a problem hive (see below). Anyway it started raining when I got to the yard so I smoked them hard and they let her walk in through the inner cover.
Are any of these good ways to introduce virgins? If not how should it be done?

My problem hive was a 4 frame nuc in May, they filled out 2 deeps and 2 meds and 1 comb super, then started making queen cells. I took the old queen and 5 frames bees and brood, left 1 capped cell. I 3 weeks I went in to see if the new queen was laying, there were lots and lots of old queen cells several had emerged, some had been tore down. No brood or eggs in the hive no queen to be found, only about 1/3 the amount of bees that there used to be. My only though is they swarmed themselves right out of business, and had a problem with the final queen who was gonna stay.