Compound tenses are formed by combining the auxiliary verb "esti" with a participle (e.g. "mi estis leganta" -> "mi legantis"). Is there ever such a thing as an infinitive form of a compound (e.g. "leganti")?
esti leg(a/i/o)nta is possible in infinitive. See this sentence from the "Ekzercaro de la Fundamento de Esperanto", mainly the part between parenthesis:
... ke tio, kion mi diris, estu vera (aŭ mi volas esti dirinta la veron).
It might also come up when you really want to emphasize the time, in sentences like:
Sen esti leginta la enhavon, mi povas aserti ke tio estas rubaĵo.
That means you have not read it in the past. That you could have but didn't. If you said:
Sen legi la enhavon, mi povas aserti ke tio estas rubaĵo.
then the meaning is more like "I can tell you right now, there is no need to read it to know that ...".
leganti is something I never found in real life. Some people use forms like legantis but not everybody is going to understand those, however logical the construction seems to be.
Plena manlibro de Esperanta gramatiko (PMEG) doesn't mention such forms at all. It takes up only A-, E- and O-forms of participles. While not officially being as high authority as Akademio de Esperanto, PMEG is for all practical purposes "the grammar book". It has lot of examples and since there are none involving any participle form with any verb ending, I would regard all those at least not-recommended, if not outright erroneous.
Remember also that the simple form mi legis is enough for most cases, and the complex form mi estis leganta is needed only, if you need to underline, to describe the state (as opposed to showing the action). E.g. Mi ĵus estis leginta pri…, kiam… okazis. : I had just read about… when… happened, but even here you can use Mi ĵus legis…