For tomato,this pest is infamous as fruit borer.So reproductive phase of plant will attract maximum infestation.Any stage from second instar onwards can be deemed suitable.
Under field condition, we often observe Helicoverpa larvae feeding on growing shoots at the early vegetative phase (within 2weeks after emergence). Therefore, I see benefits of cage installation just after crop emergence.
I already told you when fruit sets to size of a pea.Reproductive plant phase is expected about 60 DAS,However there may be early variety.so simply see flowers of yellow colour and release 10 days after that.
I think your main focus should be on the larval stage, where you have to inoculate the larvae during the vegetative stage of the host plant, preferably in cylindrical cage of cotton mesh into which the shoot tips with buds, flowers or seeds can be sleeved along with the larvae. Ensure the engulfing end of the cotton mesh (sleeve) to the plant tip or shoot is larval escape-proof (well tied into the stem and treated with sticky substance or glue to avoid larval escape or ants getting into the sleeves/cotton mesh/cage). It is important to inoculate larvae in the same stage (e.g. in the same instars). Host preference test is not only limited o the level of damage inflicted but also whether the insect will be able to complete its life cycle on the host or not and therefore, you will need to follow the different stages of the larval growth to the adult and eventually to laying eggs.