The sentence
My experience in customer service qualifies me for this position and have attached my resume for your review.
is imbalanced.
An example of another imbalanced/illogical sentence,
My chair is broken and have attached a description for the returns department to read.
To see why the sentences are imbalanced or illogical you would de-factorise the sentences. This is what I mean by factorization:
(a X b) + (a X c) => a X (b + c)
Therefore, de-factorization would be
a X (b + c) => (a X b) + (a X c)
Let's defactorize the sentence ..
My chair is broken and have attached a description =>
My chair {is broken}
and
my chair {have attached a description}
Hence, the sentence is imbalanced and illogical because
My experience in customer service qualifies me for this position
and have attached my resume for your review. =>
{My experience in customer service} {qualifies me for this position}
and
{My experience in customer service} {have attached my resume for your review}.
Therefore, to be logical, you need to write
My experience in customer service qualifies me for this position and I have attached my resume for your review.
In effect, we have removed any factorization in the sentence ...
{a X b} + {d X c} rather than (a X b) + (a X c)
Dilute self-patronage
However, being customer service as it is, you might wish to dilute any self-patronage. Being affirmative without patronising oneself, you should imply "here is my extensive experience, from which you should conclude that I qualify for the position" rather than crudely making a direct implication "here are my extensive experiences which qualify me for the job".
I have extensive experience in customer service. From the experience in customer service I have listed in my resume, I believe you would find me appropriately and adequately qualified for this position. I have attached my resume for you review.
However, employment of the subjunctive is hazardous because it projects a mood of uncertainty. It would depend on the cultural atmosphere of the organisation of that position. It should play well to small town modesty, or to be the manager of the neighbourhood Burger King. To sound more affirmative, when applying to a self-affirmative-loving metropolitan, or to a major position in a large corporate entity,
I have extensive experience in customer service which I have listed in my resume. I believe and hope you will find me appropriately and adequately qualified for this position by reviewing my experience I have listed in my resume. I am attaching my resume for your review.