The gemara[1] mentions HaMapil for one “entering to sleep on his bed,” without noting the time of day. However, the Rambam[2] writes that the beracha is recited “when one enters his bed to sleep at night.” Despite varied opinions among the Rishonim,[3] the condition of it being nighttime is accepted.[4] However, this position’s rationale impacts your question.
The above gemara continues by mentioning the berachot recited upon awakening, starting with Elokai Neshama, which some view as a “bookend” with HaMapil.[5] We recite these berachot only once a day. Although some authorities distinguish between them, in both cases there are questions as to whether these berachot are intended only for those who sleep or whether they are general praises to HaShem related to sleep and awaking at the normal times.
Most poskim rule that one recites HaMapil at night and only before serious sleep.[6] The connection to night is that this is the average person’s time of serious sleep, based on which the beracha was instituted.[7]
The B’Tzel HaChochma[8] understands the element of night very formalistically: There is no obligation, and thus no ability, to say HaMapil before night, even if one is planning a full allotment of sleep before nightfall. He compares reciting HaMapil before night to reciting the beracha on sitting in a sukka before Sukkot starts when one plans to remain there until the chag begins; a beracha is still not made before the relevant time.
However, other sources and logic indicate that night is a criterion for HaMapil on practical rather than fundamental grounds. The Chayei Adam[9] writes that the beracha is not recited before daytime sleep, because we are concerned that one will not fall asleep, daytime sleep is improper, and/or it is not effective sleep. These reasons do not apply to the cases you raise of those who have a valid reason to start sleeping before nightfall. It is possible, however, to argue that based on these common issues, HaMapil was not instituted for the daytime across the board, with no distinctions (lo plug).[10]
Several poskim[11] explain why it might be proper to recite HaMapil before one’s major sleep after dawn when one did not sleep at night (e.g., Shavuot morning). This is even more likely if one starts his night sleep during the daytime. One could add to the equation the opinion that one may recite a birkat hashevach (a beracha of praise) even when there is a doubt whether it is necessary, because the contents of such berachot are never inappropriate.[12] Nevertheless, the consensus is that the principle of safek berachot l’hakel (when in doubt about a beracha, refrain) applies to this situation as well.[13]
However, in cases in which the sleep is primarily at night, the argument to say HaMapil is much stronger. It makes sense to understand the Rambam’s statement about reciting HaMapil before going to sleep at night as meaning that the sleep done at night is the type of sleep that justifies HaMapil, not that it is inappropriate to make the beracha during the day. Thus, if the majority of one’s sleep will be during the night, the fact that it begins earlier need not preclude saying HaMapil.
It is also worthwhile to discuss the situation of one who goes to sleep soon before nightfall. Many halachot of night begin at plag hamincha.[14] Thus, one who begins his sleep for the night at that point might be considered to be extending slightly the time of night sleep. In fact, in summer nights in extreme latitudes, this is a common time to go to sleep. Note that one who wakes up after midnight may recite the morning berachot, including Elokai Neshama,[15] presumably because morning wake-up time is flexible. Maybe the converse is true in the evening. On the other hand, maybe Chazal would not have extended a beracha for going to sleep for the night to a time when one cannot fulfill the mitzva of Kri’at Shema of the night.
The rules of practical p’sak point toward not risking reciting the beracha of HaMapil before nightfall, despite the strong indications that it is called for. However, one who does recite HaMapil before his major sleep that extends well into the night has what to rely upon.