First, it is false that "intent can only be found by utilizing the dictionary they used when writing the Constitution", in fact intent can rarely be discerned by appealing to a dictionary. A better textual source is "their writings". Second, "original intent" is only one of many ideologies underlying the interpretation.
The connection between corporations and the word "person" is made because a corporation is an arrangement of some sort between natural persons. It is uncontroversial that two individuals have a constitutionally protected right to form a contract. The same protected right to form contract is recognized via case law (Trustees of Dartmouth College v. Woodward, 17 US 518), and that the charter of the college is not a relation between the government and its citizens, it is between individuals (in this case, one individual, The King, and a group of individuals).
Corporate personhood is judged on a clause-by-clause basis, always reducing to seeing (or denying) that in the particular case the corporation is (not) exercising a right on behalf of natural persons. Your own property interests and the right to a day in court to protect those rights is not diminished by dint of the interest being expressed via a collective corporate action (such as "baking and selling loaves of bread"). There are many rights of natural persons which do not extend to corporations, for example there is no 5th Amendment protection against self-incrimination. The Privileges and Immunities Clause does not extend to corporations.
It was clearly the intent of the Founders that the rights of natural persons to form contracts should not be impaired by the government, and that a person has a right to their day in court, and that is exactly what corporate-personhood doctrine recognizes – the government cannot obliterate an individual right because it is being exercised via a particular kind of agreement.