Did Imam Abu Hanifa Object to Tawassul?

Simple answer: No.

Shaykh Gibril Haddad’s Reply

Also, Allamah Ibn ‘Abidin stated in his Radd Al Muhtar:

قوله لأنه لا حق للخلق على الخالق ) قد يقال إنه لا حق لهم وجوبا على الله تعالى ، لكن الله سبحانه وتعالى جعل لهم حقا
من فضله أو يراد بالحق الحرمة والعظمة

(And his saying that there is no right of the creation on the Creator) He said that there is no right on Allah that He is compelled (wujuban) to fulfill. But Allah alloted to them rights from His grace or willingness with the right of sanctity and greatness.

Allamah Ibn ‘Abidin does discuss the permissibility of such wording though – which is not limited to merely the Prophet’s (Allah bless them all) – when discussing the hadith:

اللهم إني أسألك بحق السائلين عليك ، وبحق ممشاي إليك ، فإني لم أخرج أشرا ولا بطرا

“Oh Allah! I ask you by the right of those who ask you…”

Ibn ‘Abidins explanation was briefly mentioned in Sidi Gibrils reply.

Arabic readers can see Ibn ‘Abidins discussion here:

Rad Al Muhtar: Tawassul