No, this construction is impossible because it involves nominal syntax (*huijus domūs tēctum*), while the prepositionless gerund has verbal syntax and governs the same case as the verb (**epistolārum scrībere;* **in hōc scrībendō*). With verbs [that govern the genitive][1], in which it expresses the stimulus that evokes some feeling (memory, pity, incrimination), you can say: *eōs **prūdentiae** monēmus* > *tempus perdimus eōs **prūdentiae** monendō*. Other than that, such syntax is probably impossible even in Late Latin, where *illud epistolārum scrībere* "that writing of letters" becomes grammatical.

In the Cicero quote, **operae** is indeed the object of **pōnere**: 'to put in *some work.'* The grammar becomes more apparent if you add an explicit pronoun like ***(nescio/ali)quid** operae.*


  [1]: http://dcc.dickinson.edu/grammar/latin/genitive-verbs