Your description is vague and the best engineering design cannot be made without a complete review of the design elements in your installation. So this cannot be a recommendation.
However, based on your requirements = 2750 lbf tension and 600 lbf shear lets talk about an initial approach to the problem:
Let’s use grade 5 hardware, 85 ksi proof load, 92 ksi yield and 120 ksi tensile as an example.
Sure there is stronger stuff but these are common fasteners.
In tension, a 1/4 “ fine thread (28 tpi) bolt with a stress area of .0364” could theoretically support the tension load but fine threads aren’t recommended for aluminum. What about shear? Are you shearing across the threads or on the plain shank of the bolts?
We don’t have your answer so dividing 600 lbs by the reduced stress area of the threads. 600/.0364 = 16.5 ksi. Now shear stress limits are usually just a bit over half the tensile strength but we have unusual loading and stress concentrations pushing sideways on the threads. Figure a stress concentration of 3.0 and your shear component could be 16.5 x 3 or 49.5 ksi. That too might just barely work but there is really no factor of safety in your overall design using the ¼ -28 grade 5. (So don’t)
If you make the giant step to a 3/8” – 16, grade 5 bolt, the stress area of the threads more than doubles to .0775 sqin. The proof load is about 6500 lbf at roughly 380 in-lbs of torque and you have more than doubled your shear load. You really want to have the shear load acting through the body of the bolt and not the threads.
This 3/16” bolt might be a starting point. The nature of the loading, both magnitude and number of cycles expected can influence the design of fasteners as can corrosive environments and temperature. So we cannot guarantee the fitness of this suggestion.
It is offered as an example of preliminary bolt sizing efforts. You must either hire a professional engineer to do a complete study or take responsibility for the design yourself.
Consider using nuts and washers instead of tapping the plate if you can to increase the grip length of the bolt in tension. Threads should point down so the bolts don’t fall out if the nuts come off.