In contrary to fact conditionals in indirect discourse, the apodosis is regularly (for active verbs) rendered as future participle + fuisse.
I’m not sure it will be of much help, and I hope it isn’t more confusing than clarifying, but this is addressed in Allen & Greenough sec. 589b:
b. In changing a Condition contrary to fact (§ 517) into the Indirect Discourse, the following points require notice:—
The Protasis always remains unchanged in tense.
The Apodosis, if active, takes a peculiar infinitive form, made by combining the Participle in -ūrus with fuisse.
If the verb of the Apodosis is passive or has no supine stem, the periphrasis futūrum fuisse ut (with the Imperfect Subjunctive) must be used.
An Indicative in the Apodosis becomes a Perfect Infinitive.
Examples are:—
“nec sē superstitem fīliae futūrum fuisse, nisi spem ulcīscendae mortis êius in auxiliō commīlitōnum habuisset ” (Liv. 3.50.7) , and that he should not now be a survivor, etc., unless he had had hope, etc. [Direct: nōn superstes essem , nisi habuissem .]
“illud Asia cōgitet, nūllam ā sē neque bellī externī neque discordiārum domesticārum calamitātem āfutūram fuisse, sī hōc imperiō nōn tenērētur ” (Q. Fr. 1.1.34) , let Asia (personified) think of this, that no disaster, etc., would not be hers, if she were not held by this government. [Direct: abesset , sī nōn tenērer .]
“quid inimīcitiārum crēditis [mē] exceptūrum fuisse, sī īnsontīs lacessīssem ” (Q. C. 6.10.18) , what enmities do you think I should have incurred, if I had wantonly assailed the innocent? [excēpissem … sī lacessīssem.]
“invītum sē dīcere, nec dictūrum fuisse, nī cāritās reī pūblicae vinceret ” (Liv. 2.2) , that he spoke unwillingly and should not have spoken, did not love for the state prevail. [Direct: nec dīxissem … nī vinceret .]
“nisi eō tempore quīdam nūntiī dē Caesaris victōriā … essent allātī, exīstimābant plērīque futūrum fuisse utī [oppidum] āmitterētur ” (B. C. 3.101) , most people thought that unless at that time reports of Cæsar’s victory had been brought, the town would have been lost. [Direct: nisi essent allātī … āmissum esset .]
“quōrum sī aetās potuisset esse longinquior, futūrum fuisse ut omnibus perfectīs artibus hominum vīta ērudīrētur ” (Tusc. 3.69) , if life could have been longer, human existence would have been embellished by every art in its perfection. [Direct: sī potuisset … ērudīta esset .]
“ at plērīque exīstimant, sī ācrius īnsequī voluisset, bellum eō diē potuisse fīnīre ” (B. C. 3.51) , but most people think that, if he had chosen to follow up the pursuit more vigorously, he could have ended the war on that day. [Direct: sī voluisset … potuit .]
“Caesar respondit … sī alicûius iniūriae sibi cōnscius fuisset, nōn fuisse difficile cavēre ” (B. G. 1.14) , Cæsar replied that if [the Roman people] had been aware of any wrong act, it would not have been hard for them to take precautions. [Direct: sī fuisset , nōn difficile fuit (§ 517. c).]
[] Note 1.–I> n Indirect Discourse Present Conditions contrary to fact are not distinguished in the apodosis from Past Conditions contrary to fact, but the protasis may keep them distinct.
[] Note 2.–The periphrasis futūrum fuisse ut is sometimes used from choice when there is no necessity for resorting to it, but not in Cæsar or Cicero.
[*] Note 3.–Very rarely the Future Infinitive is used in the Indirect Discourse to express the Apodosis of a Present Condition contrary to fact. Only four or five examples of this use occur in classic authors: as,Titurius clāmābat sī Caesar adesset neque Carnutēs, etc., “neque Eburōnēs tantā cum contemptiōne nostra ad castra ventūrōs esse” (B. G. 5.29) , Titurius cried out that if Cæsar were present, neither would the Carnutes, etc., nor would the Eburones be coming to our camp with such contempt, [Direct: sī adesset … venīrent .]
I’m not sure whether this should be viewed as a special case of the “future periphrastic” construction or simply as an independent phenomenon. Apparently, according to A&G, you never find future participle + esse in present contrary to fact conditionals in indirect discourse, as the first two examples cited in A&G show. I think you would expect future participle + esse in present contrary to fact conditionals in indirect discourse if this construction were a special case of the future periphrastic construction.