[Ethereum] How to properly call getter methods from a specific keypair in web3

Since your example code uses truffle-contract you can specify the default values for your transactions and contract deployments like this (Conferrence is the name of your contract. I used the truffle default values):

Conferrence.defaults({
  from: account,
  gas: 4712388,
  gasPrice: 100000000000
})

I had the same problem (base fee exceeds gas limit) and browser-solidity gave me a Gas requirement of function xyz.sol:Xyz.doSomething(address) unknown or not constant. Specifying default values helped eventually.

I've used this scripts to deploy a contract using web3 v1.0-beta24

const Web3 = require('web3');
const web3 = new Web3('http://127.0.0.1:8545');

const ownerAddress = "0x....";
const contractAbi = [{"constant":false.... }];
const contractCode = "0x606060...";

const MyContract = new web3.eth.Contract(contractAbi);

MyContract.deploy({
  data: contractCode,
})
.send({
  from: ownerAddress,
  gas: 4000000,
  gasPrice: '30000000000000',
})
.then((instance) => {
  console.log(`Address: ${instance.options.address}`);
});

And this other script to send a message and make a query

const Web3 = require('web3');
const web3 = new Web3('http://127.0.0.1:8545');

const ownerAddress = "0x....";
const contractAbi = [{"constant":false.... }];
const contractCode = "0x606060...";
const contractAddress = "0x....";  // <----- previous script output

const myContract = new web3.eth.Contract(contractAbi, contractAddress);

const options = {
  from: ownerAddress,
  gas: 4000000,
  gasPrice: '30000000000000',
};

const message = web3.utils.asciiToHex('hola');

myContract.methods.sendMessage(message)
.send(options, (err, hash) => {
  if (err) {
    console.log(err);
  }
  console.log(`TxHash: ${hash}`);
})
.then((result) => {
  myContract.methods.getMessage().call()
  .then((result) => {
    console.log(web3.utils.hexToAscii(result));
  });
});

The sample contract I've used is very simple

pragma solidity ^0.4.18;

contract Echo {
    bytes32 public message;

    function sendMessage(bytes32 _message) public {
        message = _message;
    }

    function getMessage() view public returns (bytes32) {
        return message;
    }
}