An 80 meter dipole shortened to a length of 70 feet or less will require some type of additional matching circuit even with linear loading. The linear loading will help to reduce some of the reactive component but the resistive part of the impedance will also require some additional adjustment. This is typically done with an ATU (Antenna Tuning Unit).
Given that there is likely to be an ATU in the antenna system, there is no point in trying to increase the bandwidth of the dipole by building it in a cage configuration. The ATU will take care of any SWR bandwidth limitation by shifting the match point of the antenna system.
To maximize the performance of shortened antennas, the efficiency of the antenna system is normally of the greatest concern. This usually involves design trade-offs in impedance matching techniques. One of the most efficient methods for a shortened dipole is to use capacity hats at the end of the dipole. While this is not usable in all situations, a 40" diameter hat on the each end of your shortened dipole would go a long ways to obtaining an efficient match. Also consider the placement of the ATU and the losses in the feedline(s) due to SWR as part of your efficiency calculation.
The Chu limit is not applicable to your situation as this is typically used to be certain that the antenna can radiate the entire bandwidth of the modulated signal. Since our HF modulation methods are generally 12 KHz bandwidth or less, the calculation is meaningless. Even a very high Q antenna such as a small loop can fully handle the modulation bandwidth of HF signals. If you were considering HDTV type transmissions on UHF with a small form factor antenna, as an example, then the Chu limit might come into scope.